Palavras em English para '(algebra, ring theory, of a module) The intersection of maximal submodules of a given module.'
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noun
- (algebra, ring theory, of a module) The intersection of maximal submodules of a given module.
- (linguistics) In logographic writing systems such as the Chinese writing system, the portion of a character (if any) that provides an indication of its meaning, as opposed to phonetic.
- (organic chemistry) A free radical.
- (chemistry) A group of atoms, joined by covalent bonds, that take part in reactions as a single unit.
- (algebra, commutative algebra, ring theory, of an ideal) Given an ideal I in a commutative ring R, another ideal, denoted Rad(I) or √, such that an element x ∈ R is in Rad(I) if, for some positive integer n, xⁿ ∈ I; equivalently, the intersection of all prime ideals containing I.
- A person with radical opinions.
- (number theory) The product of the distinct prime factors of a given positive integer.
- (arithmetic) A root (of a number or quantity).
- (historical, early 20th-century France) A member of an influential, centrist political party favouring moderate social reform, a republican constitution, and secular politics.
- (linguistics) In Semitic languages, any one of the set of consonants (typically three) that make up a root.
- (algebra, ring theory, of a ring) Given a ring R, an ideal containing elements of R that share a property considered, in some sense, "not good".
- (historical, 19th-century Britain, politics) A member of the most progressive wing of the Liberal Party; someone favouring social reform (but generally stopping short of socialism).
- (linguistics) In Celtic languages, the basic, underlying form of an initial consonant which can be further mutated under the Celtic initial consonant mutations.
- a character conveying the lexical meaning of a logogram
- (linguistics) the form of a word after all affixes are removed
- an atom or group of atoms with at least one unpaired electron; in the body it is usually an oxygen molecule that has lost an electron and will stabilize itself by stealing an electron from a nearby molecule
- (chemistry) two or more atoms bound together as a single unit and forming part of a molecule
- (mathematics) a quantity expressed as the root of another quantity
- a person who has radical ideas or opinions
adj
- (mathematics) Relating to a radix or mathematical root.
- Pertaining to the basic or intrinsic nature of something.
- Thoroughgoing; far-reaching.
- (slang) Excellent; awesome.
- (chemistry, not comparable) Involving free radicals.
- (lexicography, not comparable) Of or pertaining to the root of a word.
- Favoring fundamental change, or change at the root cause of a matter.
- (phonology, phonetics, not comparable, of a sound) Produced using the root of the tongue.
- (botany, not comparable) Pertaining to a root (of a plant).
- of or relating to or constituting a linguistic root
- (used of opinions and actions) far beyond the norm
- markedly new or introducing radical change
- especially of leaves; located at the base of a plant or stem; especially arising directly from the root or rootstock or a root-like stem
- arising from or going to the root or source
noun
- (algebra, ring theory) The sum of the minimal normal submodules of a given R-module of a given ring R.
- (architecture) A low plinth or pedestal used to display a statue or other artwork.
- (architecture) A plain face or plinth at the foot of a wall.
- (group theory) The subgroup generated by the minimal normal subgroups of a given group.
- a plain plinth that supports a wall
adj
- (mathematics) Of a ring: such that all submodules of projective modules over the ring are also projective.
- Of a person: holding a legally hereditary title or rank.
- Of a title, honor or right: legally granted to somebody's descendant after that person's death.
- Passed on as an inheritance, by last will or intestate.
- Of a disease or trait: passed from a parent to offspring in the genes.
- occurring among members of a family usually by heredity
- inherited or inheritable by established rules (usually legal rules) of descent
noun
adj
- (ring theory, of a module (or algebra) over a ring) finitely generated (as a module).
- (grammar) Limited by (i.e. inflected for) person or number.
- Having an end or limit; (of a quantity) constrained by bounds; (of a set) whose number of elements is a natural number.
- bounded or limited in magnitude or spatial or temporal extent
- (of verbs) relating to forms of the verb that are limited in time by a tense and (usually) show agreement with number and person
noun
adj
- (ring theory, of an algebra or ring) Semisimple as a module over itself; equivalently, such that all (left) modules are semisimple.
- (module theory, of a module) In which each submodule is a direct summand; equivalently, equal to a direct sum of simple submodules.
- (representation theory, of a linear representation of a group or algebra) Being a direct sum of simple representations (also known as irreducible representations).
- (category theory, most generally, of an abelian category) Containing a collection of simple objects such that all objects in the category are direct sums of these simple objects.
- (Lie theory, of a Lie algebra) Being a direct sum of simple Lie algebras.
- (linear algebra, of an operator or matrix) For which every invariant subspace has an invariant complement, equivalent to the minimal polynomial being squarefree.
- (group theory, of an algebraic group) Being a linear algebraic group whose radical of the identity component is trivial.
- (of a ring, somewhat proscribed) Semiprimitive: having trivial Jacobson radical.
adj
- (algebra, of a module) Finitely generated and such that all finitely generated submodules are finitely presented.
- (algebra, of a ring) Such that every finitely generated (left) ideal is finitely presented.
- Aesthetically ordered.
- Having a natural or due agreement of parts; harmonious: a coherent design.
- (mathematics, sheaf theory, of a sheaf) Belonging to a specific class of sheaves having particularly manageable properties closely linked to the geometrical properties of the underlying space. See Coherent sheaf on Wikipedia.Wikipedia
- Orderly, logical and consistent.
- Unified; sticking together; making up a whole.
- (botany) Attaching or pressing against an organ of the same nature.
- (topology, of a topology 𝒯 on a set T with respect to a family C_a of subsets of T) In a technical sense, determined by the (topology of) the subsets. Formally, Such that 𝒯 is the finest topology on T for which the inclusion maps ιₐ:C_a→T are continuous, where each C_a is considered with its subspace topology.
- (physics) Of waves having the same direction, wavelength and phase, as light in a laser.
- marked by an orderly, logical, and aesthetically consistent relation of parts
- (physics) of waves having a constant phase relation
- sticking together
- capable of thinking and expressing yourself in a clear and consistent manner
verb
- (generally, of an algebraic structure) To be expressable as a direct sum of sub-modules, -algebras, etc.
- (algebra, transitive and intransitive, acts on a polynomial) To factor into linear factors.
- (transitive, intransitive, slang) To leave.
- (sports, especially baseball) For both teams involved in a doubleheader to win one game each and lose another.
- (intransitive, of a couple) To separate.
- (of an object which expresses the relationship between algebraic structures, particularly a short exact sequence) To contain an object which may be so expressed.
- (transitive) To share; to divide.
- To be broken; to be dashed to pieces.
- (ambitransitive) To (cause to) break up; to throw into discord.
- (intransitive, of something solid, particularly wood) To break along the grain fully or partly along a more or less straight line.
- (intransitive) To burst out laughing.
- (transitive, ergative, of something solid) To divide fully or partly along a more or less straight line.
- (intransitive, politics) To vote for candidates of opposite parties.
- come open suddenly and violently, as if from internal pressure
- discontinue an association or relation; go different ways
- go one's own way; move apart
- separate or cut with a tool, such as a sharp instrument
- separate into parts or portions
adj
- (algebra, of a short exact sequence) Having the middle object (group, module, etc.) equal to the direct sum of the others.
- (stock exchange, historical, of quotations) Given in sixteenths rather than eighths.
- (London stock exchange) Designating ordinary stock that has been divided into preferred ordinary and deferred ordinary.
- Divided.
- (of coffee) Comprising half decaffeinated and half caffeinated espresso.
- (stock exchange, of an order, sale, etc.) Divided so as to be done or executed part at one time or price and part at another time or price.
- (especially of wood) cut or ripped longitudinally with the grain
- having been divided; having the unity destroyed
noun
- A crack or longitudinal fissure.
- A dessert or confection resembling a banana split.
- (bowling) A result of a first throw that leaves two or more pins standing with one or more pins between them knocked down.
- (baseball, slang) A split-finger fastball.
- A bottle of wine containing 37.5 centiliters, half the volume of a standard 75-centiliter bottle; a demi.
- (bodybuilding) A workout routine as seen by its distribution of muscle groups or the extent and manner they are targeted in a microcycle.
- A breach or separation, as in a political party; a division.
- A unit of measure used for champagne or other spirits: 18.75 centiliters or one quarter of a standard 75-centiliter bottle. Commercially comparable to ¹⁄₂₀ (US) gallon, which is ¹⁄₂ of a fifth.
- (gymnastics, cheerleading, dance, usually in the phrase "to do the splits") A maneuver of spreading or sliding the feet apart until the legs are flat on the floor 180 degrees apart, either sideways to the body or with one leg in front and one behind, thus lowering the body completely to the floor in an upright position.
- (systematics) The division of a single taxon into two or more taxa; as opposed to a lump.
- A piece that is split off, or made thin, by splitting; a splinter; a fragment.
- (construction) A tear resulting from tensile stresses.
- (music) A recording containing songs by multiple artists; a split single or split album.
- (gambling) A division of a stake happening when two cards of the kind on which the stake is laid are dealt in the same turn.
- A split shot or split stroke.
- (athletics, speedrunning) The elapsed time at specific intermediate points in a race or speedrun.
- (leather manufacture) One of the sections of a skin made by dividing it into two or more thicknesses.
- a promised or claimed share of loot or money
- a dessert of sliced fruit and ice cream covered with whipped cream and cherries and nuts
- (tenpin bowling) a divided formation of pins left standing after the first bowl
- a lengthwise crack in wood
- a bottle containing half the usual amount
- the act of rending or ripping or splitting something
- extending the legs at right angles to the trunk (one in front and the other in back)
- an increase in the number of outstanding shares of a corporation without changing the shareholders' equity
- an opening made forcibly as by pulling apart
- division of a group into opposing factions
adj
- (algebra, of a ring) Having a unique maximal (left) ideal.
- (group theory, of a property of an infinite group) Satisfied by every finitely generated subgroup.
- (topology) Satisfied by at least one open neighborhood of every point.
- (computing, of a resource) Connected directly to a particular computer, processor, etc.; able to be accessed offline.
- (topology) Satisfied by arbitrarily small open neighborhoods of every point.
- (group theory, of a property of a finite group) Detectable from the behavior of the normalizers of the nontrivial p-subgroups.
- (algebra, algebraic geometry, of a property P of a ring R (or an R-module M)) Such that the following conditions are equivalent: (1) P holds for R (M); (2) P holds for the localization R_p (M_p) for all prime ideals p of R; (3) P holds for the localization R_m (M_m) for all maximal ideals m of R.
- (medicine) Of or pertaining to a restricted part of an organism.
- From or in a nearby location.
- (computing, of a variable or identifier) Having limited scope (either lexical or dynamic); only accessible within a certain portion of a program.
- Descended from an indigenous population.
- affecting only a restricted part or area of the body
- of or belonging to or characteristic of a particular locality or neighborhood
- relating to or applicable to or concerned with the administration of a city or town or district rather than a larger area
adv
noun
- (colloquial, medicine) Clipping of local anesthetic.
- (programming) A locally scoped identifier.
- A person who lives in or near a given place.
- (rail transport) Clipping of local train.
- A branch of a nationwide organization such as a trade union.
- (British) One's nearest or regularly frequented public house or bar.
- (fandom slang, derogatory) A Twitter user who is not a part of Stan Twitter.
- (finance) An independent trader who acts for themselves rather than on behalf of investors.
- (US, slang, journalism) An item of news relating to the place where the newspaper is published.
- public transport consisting of a bus or train that stops at all stations or stops
- anesthetic that numbs a particular area of the body
adj
- (commutative algebra, of a module M over a noetherian ring) Such that all localizations of M at maximal ideals contained in the support of M are either Cohen-Macaulay or trivial.
- (commutative algebra, of a noetherian local ring) Cohen-Macaulay as a module over itself.
- (commutative algebra, of a finite module over a noetherian local ring) Such that its depth is equal to its Krull dimension.
- (commutative algebra, of a noetherian ring) Cohen-Macaulay as a module over itself.
adj
- (module theory, of a module) Being non-trivial, and having no proper non-trivial submodules (equivalently, no proper non-trivial quotient modules).
- Uncomplicated; lacking complexity; taken by itself, with nothing added.
- Free from duplicity; guileless, innocent, straightforward.
- (botany) Not compound, but possibly lobed.
- Easy; not difficult.
- (now colloquial, euphemistic) Feeble-minded; foolish.
- (zoology) Consisting of a single individual or zooid; not compound.
- (algebra, of a Lie algebra) Being non-abelian and having no proper non-zero ideals. (Note that this is non-equivalent to the usual algebra sense; in particular, the abelian Lie algebra of dimension 1 over any given field is non-trivial and has no proper non-zero ideals, but is by convention not considered simple.)
- (mineralogy) Homogenous.
- (ring theory, of a ring) Being non-zero, and having no proper non-zero two-sided ideals (equivalently, no proper non-trivial quotient rings). For commutative rings, this definition coincides with that of a field.
- Without ornamentation; plain.
- (mathematics, real analysis, measure theory, of a real-valued function) Equal to a finite linear combination of indicator functions on measurable sets.
- (group theory, of a group) Being non-trivial, and having no proper non-trivial normal subgroups (equivalently, no proper non-trivial quotient groups).
- Undistinguished in social condition; of no special rank.
- (category theory, of an object in a category with a terminal object) Being non-isomorphic to the terminal object, and such that its only quotient objects (up to isomorphism) are the terminal object and itself.
- (chemistry, pharmacology) Consisting of one single substance; uncompounded.
- Using steam only once in its cylinders, in contrast to a compound engine, where steam is used more than once in high-pressure and low-pressure cylinders. (of a steam engine)
- (universal algebra, of an algebraic structure) Containing more than one element, and such that the only congruences on the structure are the diagonal relation (the equivalence relation a≡b⟺a=b) and the universal relation (the equivalence relation such that a≡b for all a,b). Equivalently, containing more than one element and having no proper non-trivial quotient algebras.
- exhibiting childlike simplicity and credulity
- (botany) of leaf shapes; of leaves having no divisions or subdivisions
- having few parts; not complex or complicated or involved
- apart from anything else; without additions or modifications
- easy and not involved or complicated
- lacking mental capacity and subtlety
- unornamented
noun
- (weaving) A drawloom.
- (logic) A simple or atomic proposition.
- (pharmacology) A herbal preparation made from one plant, as opposed to something made from more than one plant.
- (Roman Catholicism) A feast which is not a double or a semidouble.
- (weaving) Part of the apparatus for raising the heddles of a drawloom.
- a person lacking intelligence or common sense
- any herbaceous plant having medicinal properties
noun
- (algebra, ring theory, generalizing noun sense 5.1, with respect to a vector space V over a field F which is the field of fractions of an integral domain R in F) A finitely generated R-submodule of V which spans V over F. (In this case the submodule is called an R-lattice).
- (crystallography) A regular spacing or arrangement of geometric points, often decorated with a motif.
- (mathematics, order theory) A partially ordered set in which every pair of elements has a unique supremum and a unique infimum.
- (music) A model of the tuning relationships of a just intonation system, comprising an array of points in a periodic multidimensional pattern.
- (topology, Lie theory, generalizing noun sense 5.1) A discrete subgroup L of a given locally compact group G whose quotient space G/L has finite invariant measure.
- (heraldry) A bearing with vertical and horizontal bands that cross each other.
- A flat panel constructed with widely-spaced crossed thin strips of wood or other material, commonly used as a garden trellis.
- (group theory) A discrete subgroup of Rⁿ which is isomorphic to Zⁿ (considered as an additive group) and which spans the real vector space Rⁿ.
- an arrangement of points or particles or objects in a regular periodic pattern in 2 or 3 dimensions
- framework consisting of an ornamental design made of strips of wood or metal
- small opening (like a window in a door) through which business can be transacted
verb
adj
- (algebra, ring theory, of a ring homomorphism) Such that its target, regarded as a module over its source, is flat (as above).
- (not comparable, commerce) Of fees, fares etc., fixed; unvarying.
- Smooth; having no protrusions, indentations or other surface irregularities, or relatively so.
- (golf, of a golf club) Having a head at a very obtuse angle to the shaft.
- At a consistently depressed level; consistently lacklustre.
- (of colours) Without variation in tone or hue (uniform), and dull (not glossy).
- (music, note) Lowered by one semitone.
- In a horizontal line or plane; not sloping.
- (juggling, of a throw) Without spin; spinless.
- (algebraic geometry, scheme theory, of a morphism of schemes) Such that the induced map on every stalk is flat (as a map of rings).
- (authorship, figuratively, especially of a character) Lacking in depth, substance, or believability; underdeveloped; one-dimensional.
- (horticulture, of certain fruits) Flattening at the ends.
- (slang) Having small or invisible breasts and/or buttocks.
- (phonetics, of a vowel) Not diphthongal; without variation in height or backness.
- (of a tire or other inflated object) Deflated, especially because of a puncture.
- (homological algebra, of a module) Such that the tensor product preserves exact sequences. See Flat module on Wikipedia.Wikipedia.
- (of a battery) Unable to emit power; dead.
- (of measurements of time) Exact.
- Without variation in level, quantity, value, tone etc.
- Having no variations in height.
- (music) Of a note or voice, lower in pitch than it should be.
- (music, voice) Without variations in pitch.
- (figurative) Lacking liveliness or action; depressed; uninteresting; dull and boring.
- Absolute; downright; peremptory.
- (grammar) Not having an inflectional ending or sign, such as a noun used as an adjective, or an adjective as an adverb, without the addition of a formative suffix; or an infinitive without the sign "to".
- (wine) Lacking acidity without being sweet.
- (of coffee) Having little froth and little milk.
- (of a carbonated drink) With all or most of its carbon dioxide having come out of solution so that the drink no longer fizzes or contains any bubbles.
- sounded or spoken in a tone unvarying in pitch
- not reflecting light; not glossy
- having lost effervescence
- lacking contrast or shading between tones
- horizontally level
- stretched out and lying at full length along the ground
- having a relatively broad surface in relation to depth or thickness
- lacking taste or flavor or tang
- flattened laterally along the whole length (e.g., certain leafstalks or flatfishes)
- not modified or restricted by reservations
- commercially inactive
- lacking stimulating characteristics; uninteresting
- having a surface without slope, tilt in which no part is higher or lower than another
- (of a musical note) lowered in pitch by one chromatic semitone
- lacking the expected range or depth; not designed to give an illusion or depth
adv
- Completely, firmly, or unequivocally.
- Directly; flatly.
- (with units of time, distance, etc) Used to emphasize the smallness of the measurement.
- (finance, slang) Without allowance for accrued interest.
- Completely.
- (of accurately measured timings) Exactly, precisely.
- So as to be flat.
- (of a sentence) Without parole.
- with flat sails
- in a forthright manner; candidly or frankly
noun
- (American football) The areas behind the line of scrimmage to either side of an offensive football formation.
- (rail transport) A flat spot on the wheel of a rail vehicle.
- (publishing) A flat, glossy children's book with few pages.
- An area of level ground (sometimes covered with shallow or tidal water).
- (technical, theatre, stagecraft) A rectangular wooden structure covered with masonite, lauan, or muslin, often produced in standard modules, that is used to build wall surfaces on stage. Flats can be painted and outfitted with doors and/or windows to depict a building or other part of a scene, and are a hard-surfaced alternative to a backcloth or backdrop.
- (entomology) Any of various hesperiid butterflies that spread their wings open when they land.
- A flat sheet for use on a bed.
- (horse racing, with 'the' or attributively, sometimes with capital) Level horse-racing ground, as contrasted with courses incorporating jumps, or the racing done on such ground.
- (postal) A large mail piece measuring at least 8 1/2 by 11 inches, such as catalogs, magazines, and unfolded paper enclosed in large envelopes.
- (music) A note played one chromatic semitone lower than a natural, denoted by the symbol ♭ placed after the letter representing the note (e.g., B♭) or in front of the note symbol (e.g. ♭♪).
- (in the plural) A type of ladies' shoe with a very low heel.
- (informal, automotive) A flat tyre/flat tire.
- (painting) A thin, broad brush used in oil and watercolour painting.
- (optics) A flat (i.e. plane) mirror
- Ellipsis of flat ride (“spinning amusement ride”).
- A wide, shallow container or pallet.
- (geometry) A subset of n-dimensional space that is congruent to a Euclidean space of lower dimension.
- (in the plural) A type of flat-soled running shoe without spikes.
- The most prominent flat part of something.
- A flat-bottomed boat, without keel, and of small draught.
- (swordfighting) The flat side of a blade, as opposed to the sharp edge.
- A straw hat, broad-brimmed and low-crowned.
- A platform on a wheel, upon which emblematic designs etc. are carried in processions.
- (Australia, horse racing, with 'the' or attributively, sometimes with capital) the area in the centre of a racecourse.
- (gambling, slang) A cheater's die with the edges shaved to make certain rolls more likely.
- (in the phrase 'the flat') Level ground in general.
- (historical) An early kind of toy soldier having a flat design.
- (US) Ellipsis of flat water (“nonfizzy drinking water”).
- (chiefly British, New England, South Africa, India, Australia, New Zealand, Singapore, archaic elsewhere) A complete domicile occupying only part of a building, especially one for rent
- (Canadian Prairies, British Columbia) A 24-case of beer.
- The palm of the hand, with the adjacent part of the fingers.
- (rail transport, US) A railroad car without a roof, and whose body is a platform without sides; a platform car or flatcar.
- (mining) A horizontal vein or ore deposit auxiliary to a main vein; also, any horizontal portion of a vein not elsewhere horizontal.
- a shallow box in which seedlings are started
- a deflated pneumatic tire
- scenery consisting of a wooden frame covered with painted canvas; part of a stage setting
- a level tract of land
- a musical notation indicating one half step lower than the note named
- a suite of rooms usually on one floor of an apartment house
- freight car without permanent sides or roof
verb
- (transitive) To dash or throw
- (poker slang) To make a flat call; to call without raising.
- (intransitive) To become flat or flattened; to sink or fall to an even surface.
- (intransitive, music, colloquial) To fall from the pitch.
- (intransitive) To dash, rush
- (transitive, music) To depress in tone, as a musical note; especially, to lower in pitch by half a tone.
adj
- (commutative algebra, of a ring) Such that all of its localizations at prime ideals are integrally closed domains.
- (topology, of a topology or topological space) In which disjoint closed sets can be separated by disjoint neighborhoods.
- (linear algebra, of a matrix) Which commutes with its conjugate transpose.
- (complex analysis, of a family of continuous functions) Which is pre-compact.
- (commutative algebra, of a domain) Integrally closed: equal its own integral closure in its field of fractions.
- (functional analysis, of a Hilbert space operator) Which commutes with its adjoint.
- (probability theory, statistics, of a distribution, random variable, etc.) Which has a very specific bell curve shape; that is or has the qualities of a normal distribution.
- (physics, of a mode in an oscillating system) In which all parts of an object vibrate at the same frequency (a normal mode).
- (rail transport, of points) In the default position, set for the most frequently used route.
- (chemistry) Of, relating to, or being a solution containing one equivalent weight of solute per litre of solution.
- (category theory, of a category) Which contains only normal morphisms.
- (organic chemistry) Describing a straight chain isomer of an aliphatic hydrocarbon, or an aliphatic compound in which a substituent is in the 1- position of such a hydrocarbon.
- (fandom slang, sarcastic, with “about”) Fervently interested in a subject; obsessed.
- (algebraic geometry, of a variety or scheme) Such that the local ring at every point is an integrally closed domain.
- (category theory, of a morphism) Which is the kernel or cokernel of some morphism, respectively.
- (number theory, of a real number) In whose representation in a given base b ≥ 2, for every positive integer n, the bⁿ possible strings of n digits follow a uniform distribution.
- Usual, healthy; not sick or ill or unlike oneself.
- (set theory, of a function from the ordinals to the ordinals) Which is strictly monotonically increasing and continuous with respect to the order topology.
- (algebra, of a field extension of a field K) Which is the splitting field of a family of polynomials in K.
- (algebra, of a subgroup) With cosets which form a group.
- (education, of a school) Teaching teachers how to teach; teaching teachers the norms of education.
- According to norms or rules or to a regular pattern.
- (geometry) Perpendicular to a tangent of a curve or tangent plane of a surface.
- in accordance with scientific laws
- conforming with or constituting a norm or standard or level or type or social norm; not abnormal
- forming a right angle
- being approximately average or within certain limits in e.g. intelligence and development
noun
- (geometry, countable) A line or vector that is perpendicular to another line, surface, or plane.
- (medicine, countable) A person who is healthy, normal, as opposed to one who is morbid.
- (slang, countable) A person who is normal, who fits into mainstream society, as opposed to those who live alternative lifestyles.
- (countable, uncountable) The usual state.
- something regarded as a normative example
adj
- (algebra, module theory, of a (left) module M over a ring R) Loosely, having a certain generalizing property, abstracted from the study of ℚ as a ℤ-module. Formally, such that any short exact sequence of (left) R-modules beginning with M splits, or any of several equivalent statements: See Injective module.
- (homological algebra, of a resolution) Such that the objects (usually modules) involved in the resolution are injective (in the algebraic senses above).
- (mathematics) Of, relating to, or being an injection: such that each element of the image (or range) is associated with at most one element of the preimage (or domain); inverse-deterministic
- (category theory, most generally, of an object Q in a category C) Loosely, having a property analogous to that which characterizes injective modules (see above). Formally, such that, given a monomorphism f:X→Y in C, for every morphism g:X→Q there exists a morphism h:Y→Q such that h∘f=g; see Injective object.
adv
- (algebra) Of a subgroup of finite index.
- By computer or in cyberspace.
- (topology) Of a covering space of finite degree.
- Almost but not quite.
- In essence or functionally, but not in fact, formally, or technically.
- in essence or effect but not in fact
- (of actions or states) slightly short of or not quite accomplished; all but
adj
- (algebra, commutative algebra, of a ring element in a ring B relative to a subring A) Being the root of some monic polynomial in A.
- Constituting a whole together with other parts or factors; not omittable or removable.
- (mathematics) Relating to integration (“the process of finding the integral [noun] of a function”).
- (mathematics) Of, pertaining to, or being an integer.
- constituting the undiminished entirety; lacking nothing essential especially not damaged
- of or denoted by an integer
- existing as an essential constituent or characteristic
noun
- (mathematics) One of the two fundamental operations of calculus (the other being differentiation), whereby a function's displacement, area, volume, or other qualities arising from the study of infinitesimal change are quantified, usually defined as a limiting process on a sequence of partial sums. Denoted using a long s: ∫, or a variant thereof.
- (mathematics) A definite integral: the result of the application of such an operation onto a function and a suitable subset of the function's domain: either a number or positive or negative infinity. In the former case, the integral is said to be finite or to converge; in the latter, the integral is said to diverge. In notation, the domain of integration is indicated either below the sign, or, if it is an interval, with its endpoints as sub- and super-scripts, and the function being integrated forming part of the integrand (or, generally, differential form) appearing in front of the integral sign.
- (specifically) Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc.
- (mathematics) An indefinite integral: the result of the application of such an operation onto a function together with an indefinite domain, yielding a function; a function's antiderivative;
- the result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x)
adj
- (algebra, of a nonzero module) Such that the annihilator of any nonzero submodule is equal to the annihilator of the whole module.
- Early; blooming; being in the first stage.
- First in excellence, quality, or value.
- First in importance, degree, or rank.
- First in time, order, or sequence.
- (algebra, of an ideal) Having its complement closed under multiplication.
- Marked or distinguished by the prime symbol.
- (mathematics, technical) Such that if it divides a product, it divides one of the multiplicands.
- (mathematics, lay) Having exactly two integral factors: itself and unity (1 in the case of integers).
- used of the first or originating agent
- being at the best stage of development
- first in rank or degree
- of or relating to or being an integer that cannot be factored into other integers
- of superior grade
noun
- (Christianity) The religious service appointed to this hour.
- (historical) The first hour of daylight; the first canonical hour.
- The symbol ′ used to indicate feet, minutes, derivation and other measures and mathematical operations.
- (algebra, number theory) A prime element of a mathematical structure, particularly a prime number.
- The most active, thriving, or successful stage or period.
- A feather, from the wing of the cock ostrich, that is of the palest possible shade.
- (psychology) A stimulus which causes priming.
- The chief or best individual or part.
- An inch, as composed of twelve seconds in the duodecimal system.
- (backgammon) A series of consecutive blocks. A prime of six prevents the opponent's pieces from passing.
- (fencing) The first defensive position, with the sword hand held at head height, and the tip of the sword at head height.
- (card games) A four-card hand containing one card of each suit in the game of primero; the opposite of a flush in poker.
- Something which is first in importance or rank: a prime defense company, mortgage lender, etc.
- (film) Contraction of prime lens, a film lens.
- (cycling) An intermediate sprint within a race, usually offering a prize and/or points.
- (music) The first note or tone of a musical scale.
- the period of greatest prosperity or productivity
- a natural number that has exactly two distinct natural number divisors: 1 and itself
- the second canonical hour; about 6 a.m.
- the time of maturity when power and vigor are greatest
verb
- (mathematics) To mark with a prime mark.
- (transitive) To fill or prepare the chamber of a mechanism for its main work.
- To apply priming to (a musket or cannon); to apply a primer to (a metallic cartridge).
- (intransitive, of a steam boiler) To work so that foaming occurs from too violent ebullition, which causes water to become mixed with, and be carried along with, the steam that is formed.
- (intransitive) To serve as priming for the charge of a gun.
- To prepare; to make ready.
- (transitive) To apply a coat of primer paint to.
- fill with priming liquid
- cover with a primer; apply a primer to
- insert a primer into (a gun, mine, or charge) preparatory to detonation or firing
noun
- (algebra, ring theory) An invariant of rings and modules, encoding information about dimensionality; see Depth (ring theory).
- the most severe part
- the vertical distance below a surface; the degree to which something is deep
- (statistics) the lower of the two ranks of a value in an ordered set of values
- lowness
- (literary, usually in the plural) the deepest part (usually of a body of water)
- (logic) the number of simple elements which an abstract conception or notion includes; the comprehension or content
- the distance between the front and the back, as the depth of a drawer or closet
- (horology) a pair of toothed wheels which work together
- (art, photography) the property of appearing three-dimensional
- (cryptography) A set of more than one ciphertext enciphered with the same key.
- (computing, colors) the total palette of available colors
- (aeronautics) the perpendicular distance from the chord to the farthest point of an arched surface
- (figuratively) the intensity, complexity, strength, seriousness or importance of an emotion, situation, etc.
- (literary, usually in the plural) a very remote part.
- (usually plural) a low moral state
- the attribute or quality of being deep, strong, or intense
- degree of psychological or intellectual profundity
- the intellectual ability to penetrate deeply into ideas
- the extent downward or backward or inward
adj
- (of a module) In which any ascending chain of submodules eventually becomes constant.
- (of a topological space) In which any ascending chain of open subsets eventually becomes constant.
- (algebraic geometry, of a scheme) admitting a finite covering by open affine subsets operatorname SpecA_i, where each A_i is a noetherian ring;
- (mathematics, of a binary relation on a set) Such that the converse relation is well-founded (on that set).
- (of a group) In which any ascending chain of subgroups eventually becomes constant.
- (of a ring) In which any ascending chain of ideals eventually becomes constant.
adj
- (commutative algebra, not comparable, of a local ring) Noetherian and such that the minimal number of generators of the maximal ideal is equal to the Krull dimension of the ring.
- Demonstrating a consistent set of rules; showing order, evenness of operation or occurrence.
- (botany, zoology) Having all the parts of the same kind alike in size and shape.
- (chiefly US) Having the expected characteristics or appearances; normal, ordinary, standard.
- (geometry, of a polygon) Both equilateral and equiangular; having all sides of the same length, and all (corresponding) angles of the same size
- (astronomy) Of a moon or other satellite: following a relatively close and prograde orbit with little inclination or eccentricity.
- (Christianity) Bound by religious rule; belonging to a monastic or religious order (often as opposed to secular).
- (mathematical analysis, not comparable, of a Borel measure) Such that every set in its domain is both outer regular and inner regular.
- (colloquial) Exemplary; excellent example of; utter, downright.
- Happening at constant (especially short) intervals.
- (chiefly military) Permanently organised; being part of a set professional body of troops.
- Having bowel movements or menstrual periods at constant intervals in the expected way.
- (snowboarding) Riding with the left foot forward.
- (geometry, of a polyhedron) Whose faces are all congruent regular polygons, equally inclined to each other.
- (crystallography) Isometric.
- (algebraic geometry, not comparable, of a scheme) Such that the local ring at every point is regular.
- (grammar, of a verb, plural, etc) Following a set or common pattern; according to the general rules of a given language.
- Having a constant pattern; showing evenness of form or appearance.
- officially full-time
- in accordance with fixed order or procedure or principle
- regularly scheduled for fixed times
- symmetrically arranged
- conforming to a standard or pattern
- (used of the military) belonging to or engaged in by legitimate army forces
- not constipated
- in accord with regular practice or procedure
- relating to a person who does something regularly
- not deviating from what is normal
- often used as intensifiers
- occurring at fixed intervals
- (of solids) having clear dimensions that can be measured; volume can be determined with a suitable geometric formula
noun
- (Singapore) Synonym of regular serviceman; a member of the Singapore Armed Forces, Police Force or Civil Defence Force who has signed on, i.e., chosen to work full-time beyond their required length of national service.
- Anything that is normal or standard.
- A frequent customer, client or business partner.
- (Canada) A coffee with one cream and one sugar.
- A member of the armed forces or police force.
- A fixed number for each month serving to ascertain the day of the week, or the age of the moon, on the first day of any month.
- A member of the British Army (as opposed to a member of the Territorial Army or Reserve).
- A frequent, routine visitor to an establishment.
- A member of a religious order who has taken the three ordinary vows.
- A number for each year, giving, added to the concurrents, the number of the day of the week on which the Paschal full moon falls.
- (television) A character who appears in every episode of a TV series; a member of the regular cast.
- a soldier in the regular army
- a dependable follower (especially in party politics)
- a regular patron
- a garment size for persons of average height and weight
noun
- (algebra, ring theory) An algebraic structure similar to a ring, but without the requirement that every element have an additive inverse.
- A promiscuous woman.
- (slang) Equipment used for taking recreational drugs.
- (slang, computing) A personal computer, typically one modified for looks.
- The special apparatus used for drilling wells.
- (US) A large truck, especially a semi-trailer truck.
- (slang) Radio equipment, especially a citizen's band transceiver.
- (nautical) The rigging of a sailing ship or other such craft.
- An imperfectly castrated horse, sheep etc.
- (informal) A costume or an outfit.
- (Northern England, Scotland, dialect) A ridge.
- Special equipment or gear used for a particular purpose.
- (animation) A model outfitted with parameterized controls for animation.
- a set of clothing (with accessories)
- gear used in fishing
- formation of masts, spars, sails, etc., on a vessel
- the act of swindling by some fraudulent scheme
- a truck consisting of a tractor and trailer together
- gear (including necessary machinery) for a particular enterprise
- a vehicle with wheels drawn by one or more horses
verb
- (transitive, intransitive, animation) To outfit a model with controls for animation.
- (transitive, manufacturing) To move (a heavy object) with the help of slings, hoists, block and tackle, levers, or similar equipment.
- (transitive) To manipulate something dishonestly for personal gain or discriminatory purposes.
- (transitive) To make or construct something in haste or in a makeshift manner.
- (transitive, informal) To dress or clothe in some costume.
- (transitive, nautical) To equip and fit (a ship) with sails, shrouds, and yards.
- equip with sails or masts
- manipulate in a fraudulent manner
- connect or secure to
- arrange the outcome of by means of deceit
noun
- (commutative algebra, of a module M over a commutative ring R) The set of all prime ideals of R such that the localization of M at the prime is nonzero, denoted operatorname SuppM
- (sometimes attributive) Something which supports.
- An accompaniment in music.
- Evidence.
- (fuzzy set theory) A set whose elements are at least partially included in a given fuzzy set (i.e., whose grade of membership in that fuzzy set is strictly greater than zero).
- (mathematics) in relation to a function, the set of points where the function is not zero; the closure of that set.
- (structural analysis) Horizontal, vertical or rotational support of structures: movable, hinged, fixed.
- An actor playing a subordinate part with a star.
- (computing) Compatibility and functionality for a given product or feature.
- Answers to questions and resolution of problems regarding something sold.
- Financial or other help.
- (gymnastics) Clipping of support position.
- financial resources provided to make some project possible
- any device that bears the weight of another thing
- the act of bearing the weight of or strengthening
- supporting structure that holds up or provides a foundation
- a military operation (often involving new supplies of men and materiel) to strengthen a military force or aid in the performance of its mission
- aiding the cause or policy or interests of
- the activity of providing for or maintaining by supplying with money or necessities
- something providing immaterial assistance to a person or cause or interest
- the financial means whereby one lives
- a musical part (vocal or instrumental) that supports or provides background for other musical parts
- documentary validation
verb
- (transitive) To answer questions and resolve problems regarding something sold.
- (transitive) To serve, as in a customer-oriented position; to give support to.
- (transitive) To provide evidence for; to lend credibility to.
- (transitive) To provide sustenance or maintenance for; to sustain in integrity or livelihood.
- (transitive) To back or favor a cause, party, etc., mentally or with concrete aid:
- (transitive) To help keep from falling.
- (transitive) To play a lesser part in the same production with (a star performer).
- (transitive) To assist or be involved with, but not be responsible for.
- (transitive) To help, particularly financially; to subsidize.
- (transitive, said of electronic devices, programming languages, etc.) To be designed to provide capacity for; to work or be compatible with (a part, accessory, file type, program, algorithm, etc.).
- be the physical support of; carry the weight of
- be a regular customer or client of
- put up with something or somebody unpleasant
- argue or speak in defense of
- support with evidence or authority or make more certain or confirm
- adopt as a belief
- give moral or psychological support, aid, or courage to
- establish or strengthen as with new evidence or facts
- play a subordinate role to (another performer)
- be behind; approve of
- support materially or financially
noun
- An algebraic structure consisting of a module over a commutative ring (or a vector space over a field) along with an additional binary operation that is bilinear over module (or vector) addition and scalar multiplication.
- (figurative) A system or process (especially one that is complex or convoluted) that substitutes one thing for another, or uses signs or symbols to represent concepts or ideas.
- (countable, set theory, mathematical analysis) A collection of subsets of a given set, such that this collection contains the empty set, and the collection is closed under unions and complements (and thereby also under intersections and differences).
- (uncountable, mathematics, sometimes capitalized) Abstract algebra: A broad field of study in modern mathematics (often mentioned alongside analysis) loosely characterized by its concern for abstraction and symmetry, dealing with the behavior, classification, and application of a large class of objects (called algebraic structures) and the maps between them (called, most generally, morphisms).
- (uncountable, medicine, historical, rare) The surgical treatment of a dislocated or fractured bone. Also (countable): a dislocation or fracture.
- (uncountable, mathematics) Elementary algebra: A system for representing and manipulating unknown quantities (variables) in equations.
- A universal algebra.
- the mathematics of generalized arithmetical operations
noun
- (algebra) A ring of fractions of a given ring, such that the complement of the set of allowed denominators is an ideal.
- (algebra) A systematic method of adding multiplicative inverses to a ring.
- (software engineering) The act, process, or result of making a product suitable for use in a particular country or region.
- (translation studies, chiefly software, marketing) The act, process, or result of adapting translated text to fit a local culture; domestication.
- The act of localizing.
- (Hong Kong politics, specifically) The switch of positions in power from the colonizing population to the local population.
- The state of being localized.
- (physiology) the principle that specific functions have relatively circumscribed locations in some particular part or organ of the body
- a determination of the place where something is
noun
- (algebra, ring theory) Initialism of central simple algebra.
- (countable) Initialism of community service announcement.
- (uncountable) Initialism of child sexual abuse.
- (US) Initialism of combined statistical area.
- (algebra, Lie theory) Initialism of Cartan subalgebra.
- (uncountable) Initialism of community-supported agriculture.
name
- (Northern Ireland) Initialism of Central Services Agency.
- (British) Initialism of Child Support Agency.
- (Canada, space flight) Initialism of Canadian Space Agency.
- (Canada) Initialism of Canadian Standards Association.
- (US) Initialism of Confederate States of America.
- (US) Initialism of Controlled Substances Act.
adj
noun
verb
adj
- (ring theory, of a local ring) Complete as a topological group with respect to its m-adic topology, where m is its unique maximal idea.
- (algebra, of a lattice) In which every set with a lower bound has a greatest lower bound.
- (computing theory, of a problem) That is in a given complexity class and is such that every other problem in the class can be reduced to it (usually in polynomial time or logarithmic space).
- With all parts included; with nothing missing; full.
- (logic, of a proof system of a formal system with respect to a given semantics) In which every semantically valid well-formed formula is provable.
- Generic intensifier.
- Finished; ended; concluded; completed.
- (mathematics, of a category) In which all small limits exist.
- (mathematical analysis, of a metric space or topological group) In which every Cauchy sequence converges to a point within the space.
- having every necessary or normal part or component or step
- highly skilled
- without qualification; used informally as (often pejorative) intensifiers
- having come or been brought to a conclusion
- perfect and complete in every respect; having all necessary qualities
noun
verb
- (transitive) To make whole or entire.
- (poker) To call from the small blind in an unraised pot.
- (ambitransitive) To finish; to make done; to reach the end.
- come or bring to a finish or an end
- write all the required information onto a form
- complete or carry out
- bring to a whole, with all the necessary parts or elements
- complete a pass
noun
- (mathematics, algebra) The additive identity element of a monoid or greater algebraic structure, particularly a group or ring.
- (mathematics) A value of the independent variables of a function, for which the function is equal to zero.
- The value of a magnitude corresponding to the cardinal number zero.
- (informal, uncountable) Nothing, or none.
- The numeric symbol that represents the cardinal number zero.
- The point on a scale at which numbering or measurement originates.
- (slang) A person dismissed as unimportant.
- (finance) A security which has a zero coupon (paying no periodic interest).
- The digit 0 in the decimal, binary, and all other base numbering systems.
- (military, usually capitalized) A Mitsubishi A6M Zero, a long range fighter aircraft operated by the Imperial Japanese Navy Air Service from 1940 to 1945.
- A setting of calibrated instruments such as a firearm, corresponding to a zero value.
- a quantity of no importance; thing (object:), singular, negative pronoun; pronoun, thing, singular; quantifier: negative existential
- the point on a scale from which positive or negative numerical quantities can be measured
- the sight setting that will cause a projectile to hit the center of the target with no wind blowing
- a mathematical element that when added to another number yields the same number
adj
- (meteorology) Of a cloud ceiling, limiting vision to 50 feet (15 meters) or less.
- (linguistics) Present at an abstract level, but not realized in the surface form.
- (meteorology) Of horizontal visibility, limited to 165 feet (50.3 meters) or less.
- (postpositive) Used in the names of foodstuffs, especially beverages, to indicate a version with no calories
- of or relating to the null set (a set with no members)
- having no measurable or otherwise determinable value
- indicating the absence of any or all units under consideration
- indicating an initial point or origin
det
num
verb
noun
- (mathematics, linear algebra) A relation between generators of a module.
- (Jungian psychology) An archetypal pairing of contrasexual opposites, symbolizing the communication of the conscious and unconscious minds.
- (astronomy, astrology) An alignment of three celestial bodies (for example, the Sun, Earth, and Moon) such that one body is directly between the other two, such as occurs at an eclipse.
- (zoology) The association of two protozoa end-to-end or laterally for the purpose of asexual exchange of genetic material.
- (Gnosticism) Complementary female–male pairings of the emanations known as Aeons.
- (genetics) The pairing of chromosomes in meiosis.
- (medicine) The fusion of some or all of the organs.
- the straight line configuration of 3 celestial bodies (as the sun and earth and moon) in a gravitational system
noun
- (algebra, ring theory) A two-sided ideal; a subset of a ring which is closed under both left and right multiplication by elements of the ring.
- (algebra) A subsemigroup with the property that if any semigroup element outside of it is added to any one of its members, the result must lie outside of it.
- (algebra, order theory, lattice theory) A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).
- A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
- (algebra, Lie theory) A Lie subalgebra (subspace that is closed under the Lie bracket) 𝖍 of a given Lie algebra 𝖌 such that the Lie bracket [𝖌,𝖍] is a subset of 𝖍.
- (set theory) A collection of sets, considered small or negligible, such that every subset of each member and the union of any two members are also members of the collection.
- model of excellence or perfection of a kind; one having no equal
- the idea of something that is perfect; something that one hopes to attain
adj
- Existing only in the mind; conceptual, imaginary.
- Optimal; being the best possibility.
- Teaching or relating to the doctrine of idealism.
- Pertaining to ideas, or to a given idea.
- Perfect, flawless, having no defects.
- (mathematics) Not actually present, but considered as present when limits at infinity are included.
- of or relating to the philosophical doctrine of the reality of ideas
- conforming to an ultimate standard of perfection or excellence; embodying an ideal
- constituting or existing only in the form of an idea or mental image or conception
noun
- (algebra, somewhat humorous) An associated prime of a module.
- Someone who intentionally kills a person, especially a professional who kills a public or political figure.
- (historical, usually capitalized) A member of the Nizari Ismaili Muslim community of the Alamut Period.
- Any ruthless killer.
- a murderer (especially one who kills a prominent political figure) who kills by a surprise attack and often is hired to do the deed
- a member of a secret order of Muslims (founded in the 12th century) who terrorized and killed Christian Crusaders
verb
noun
- (algebra, group theory, ring theory) The set of those elements (of a given algebraic structure) that commute with every other element, usually denoted Z(G). In the case of (semi-)groups, it is required that they commute under the (semi-)group operation; in the case of rings and (Lie) algebras, under multiplication (i.e. the bracket for Lie algebras)
- A place, especially a building or complex, set aside for some specified function or activity.
- (engineering) A conical recess or indentation in the end of a shaft or other work, to receive the point of a center, on which the work can turn, as in a lathe.
- (American football, Canadian football) The person who holds the ball at the beginning of each play.
- (geometry) The point in the interior of any figure of any number of dimensions that has as its coordinates the arithmetic mean of the coordinates of all points on the perimeter of the figure (or of all points in the interior for a center of volume).
- (basketball) The player, generally the tallest, who plays closest to the basket.
- (ice hockey) The forward that generally plays between the left wing and right wing and usually takes the faceoffs.
- (geometry) A point on a triangle's plane that is in some sense in its middle.
- The point in the interior of a sphere that is equidistant from all points on the circumference.
- The point in the interior of a circle that is equidistant from all points on the circumference.
- The middle portion of something; the part well away from the edges.
- (netball) A player who can go all over the court, except the shooting circles.
- (Australia, New Zealand) The ring in the gambling game two-up in which the spinner operates.
- (soccer) A pass played into the centre of the pitch.
- (rugby) One of the backs operating in a central area of the pitch, either the inside centre or outside centre.
- A topic that is particularly important in a given context, the element in a subject of cognition, volition or discussion that is perceived as decisive.
- (geometry) The point on a line that is midway between the ends.
- (engineering) One of the two conical steel pins in a lathe, etc., upon which the work is held, and about which it revolves.
- The venue in which the head of government in a centralized state is situated.
- (politics) The ensemble of moderate or centrist political parties.
- (architecture) A temporary structure upon which the materials of a vault or arch are supported in position until the work becomes self-supporting.
- (ice hockey) the person who plays center on a hockey team
- politically moderate persons; centrists
- the position on a hockey team of the player who participates in the face off at the beginning of the game
- (football) the person who plays center on the line of scrimmage and snaps the ball to the quarterback
- mercantile establishment consisting of a carefully landscaped complex of shops representing leading merchandisers; usually includes restaurants and a convenient parking area; a modern version of the traditional marketplace
- a place where some particular activity is concentrated
- the middle of a military or naval formation
- a position on a basketball team of the player who participates in the jump that starts the game
- the piece of ground in the outfield directly ahead of the catcher
- the object upon which interest and attention focuses
- (American football) the position of the player on the line of scrimmage who puts the ball in play
- a point equidistant from the ends of a line or the extremities of a figure
- (basketball) the person who plays center on a basketball team
- the choicest or most essential or most vital part of some idea or experience
- a building dedicated to a particular activity
- an area that is approximately central within some larger region
- a cluster of nerve cells governing a specific bodily process
- the sweet central portion of a piece of candy that is enclosed in chocolate or some other covering
adj
verb
- (transitive) To give (something) a central basis.
- (intransitive) To concentrate on (something), to pay close attention to (something).
- (transitive) To cause (some attribute, such as a mood or voltage) to be adjusted to a value which is midway between the extremes.
- (transitive) To cause (an object) to occupy the center of an area.
- (engineering) To form a recess or indentation for the reception of a center.
- direct one's attention on something
- center upon
- move into the center
noun
- (algebraic topology, homological algebra, more generally) An element of a group (or module) in a chain complex.
- A livery collar, a chain of office.
- A unit of length, exactly equal to 22 yards, which is 4 rods or 100 links, and approximately equal to 20.12 metres; the length of a Gunter's surveying chain; the length of a cricket pitch.
- That which confines, fetters, or secures; a bond.
- A series of stores or businesses with the same brand name.
- A series of interconnected things.
- (weaving) The warp threads of a web.
- (British) A sequence of linked house purchases, each of which is dependent on the preceding and succeeding purchase (said to be "broken" if a buyer or seller pulls out).
- (surveying) A series of interconnected links of known length, used as a measuring device.
- A series of interconnected rings or links usually made of metal.
- (surveying) A long measuring tape.
- (mathematics, set theory, order theory) A totally ordered set, especially a totally ordered subset of a poset.
- (nautical, in the plural) Iron links bolted to the side of a vessel to bold the dead-eyes connected with the shrouds; also, the channels.
- (algebraic topology, originally) A formal sum of cells in a CW complex of a certain dimension k (in which case the formal sums are called k'''-chains); a formal sum of simplices or cubes of a certain dimension in a simplical complex or cubical complex (respectively).
- (organic chemistry, physical chemistry) A number of atoms in a series, which combine to form a molecule.
- a unit of length
- a series of things depending on each other as if linked together
- (chemistry) a series of linked atoms (generally in an organic molecule)
- anything that acts as a restraint
- a series of (usually metal) rings or links fitted into one another to make a flexible ligament
- a necklace made by stringing objects together
- a linked or connected series of objects
- (business) a number of similar establishments (stores or restaurants or banks or hotels or theaters) under one ownership
- a series of hills or mountains
verb
- (computing) To be chained to another data item.
- (transitive, computing, rare, associated with Acorn Computers) To load and automatically run (a program).
- (intransitive) To link multiple items together.
- (figurative) To connect as if with a chain, due to dependence, addiction, or other feelings
- (computing) To relate data items with a chain of pointers.
- (transitive) To measure a distance using a 66-foot long chain, as in land surveying.
- (figurative) To obligate.
- (transitive) To secure someone with fetters.
- (transitive) To fasten something with a chain.
- (transitive) To obstruct the mouth of a river etc with a chain.
- fasten or secure with chains
- connect or arrange into a chain by linking
adj
- (commutative algebra, of a filtration (M_n) of a module M over a ring with respect to an ideal (here I but often a,m,p etc.) of that ring) Eventually satisfying the identity IM_n=M_n+1.
- (computer science, of a sorting algorithm) That maintains the relative order of items that compare as equal.
- (computing) Of software: established to be relatively free of bugs, as opposed to a beta version.
- Relatively unchanging, steady, permanent; firmly fixed or established; consistent; not easily moved, altered, or destroyed.
- firm and dependable; subject to little fluctuation
- showing little if any change
- resistant to change of position or condition
- not taking part readily in chemical change
- maintaining equilibrium
noun
- (professional wrestling) A group of wrestlers who support each other within a wrestling storyline.
- A building, wing or dependency set apart and adapted for lodging and feeding (and training) ungulates, especially horses.
- (slang) A group of prostitutes managed by one pimp.
- A group of people who are looked after, mentored, or trained in one place or for a particular purpose or profession.
- A coherent or consistent set of things (typically abstract) available or presented; array.
- (sumo) An organization of sumo wrestlers who live and train together.
- (Scotland) A set of advocates; a barristers' chambers.
- (metonymic) All the racehorses of a particular stable, i.e. belonging to a given owner.
- a farm building for housing horses or other livestock
verb
noun
- (algebra, ring theory, of a module) The intersection of maximal submodules of a given module.
- (linguistics) In logographic writing systems such as the Chinese writing system, the portion of a character (if any) that provides an indication of its meaning, as opposed to phonetic.
- (organic chemistry) A free radical.
- (chemistry) A group of atoms, joined by covalent bonds, that take part in reactions as a single unit.
- (algebra, commutative algebra, ring theory, of an ideal) Given an ideal I in a commutative ring R, another ideal, denoted Rad(I) or √, such that an element x ∈ R is in Rad(I) if, for some positive integer n, xⁿ ∈ I; equivalently, the intersection of all prime ideals containing I.
- A person with radical opinions.
- (number theory) The product of the distinct prime factors of a given positive integer.
- (arithmetic) A root (of a number or quantity).
- (historical, early 20th-century France) A member of an influential, centrist political party favouring moderate social reform, a republican constitution, and secular politics.
- (linguistics) In Semitic languages, any one of the set of consonants (typically three) that make up a root.
- (algebra, ring theory, of a ring) Given a ring R, an ideal containing elements of R that share a property considered, in some sense, "not good".
- (historical, 19th-century Britain, politics) A member of the most progressive wing of the Liberal Party; someone favouring social reform (but generally stopping short of socialism).
- (linguistics) In Celtic languages, the basic, underlying form of an initial consonant which can be further mutated under the Celtic initial consonant mutations.
- a character conveying the lexical meaning of a logogram
- (linguistics) the form of a word after all affixes are removed
- an atom or group of atoms with at least one unpaired electron; in the body it is usually an oxygen molecule that has lost an electron and will stabilize itself by stealing an electron from a nearby molecule
- (chemistry) two or more atoms bound together as a single unit and forming part of a molecule
- (mathematics) a quantity expressed as the root of another quantity
- a person who has radical ideas or opinions
adj
- (mathematics) Relating to a radix or mathematical root.
- Pertaining to the basic or intrinsic nature of something.
- Thoroughgoing; far-reaching.
- (slang) Excellent; awesome.
- (chemistry, not comparable) Involving free radicals.
- (lexicography, not comparable) Of or pertaining to the root of a word.
- Favoring fundamental change, or change at the root cause of a matter.
- (phonology, phonetics, not comparable, of a sound) Produced using the root of the tongue.
- (botany, not comparable) Pertaining to a root (of a plant).
- of or relating to or constituting a linguistic root
- (used of opinions and actions) far beyond the norm
- markedly new or introducing radical change
- especially of leaves; located at the base of a plant or stem; especially arising directly from the root or rootstock or a root-like stem
- arising from or going to the root or source
noun
- (algebra, ring theory) The sum of the minimal normal submodules of a given R-module of a given ring R.
- (architecture) A low plinth or pedestal used to display a statue or other artwork.
- (architecture) A plain face or plinth at the foot of a wall.
- (group theory) The subgroup generated by the minimal normal subgroups of a given group.
- a plain plinth that supports a wall
noun
- (algebra, ring theory, generalizing noun sense 5.1, with respect to a vector space V over a field F which is the field of fractions of an integral domain R in F) A finitely generated R-submodule of V which spans V over F. (In this case the submodule is called an R-lattice).
- (crystallography) A regular spacing or arrangement of geometric points, often decorated with a motif.
- (mathematics, order theory) A partially ordered set in which every pair of elements has a unique supremum and a unique infimum.
- (music) A model of the tuning relationships of a just intonation system, comprising an array of points in a periodic multidimensional pattern.
- (topology, Lie theory, generalizing noun sense 5.1) A discrete subgroup L of a given locally compact group G whose quotient space G/L has finite invariant measure.
- (heraldry) A bearing with vertical and horizontal bands that cross each other.
- A flat panel constructed with widely-spaced crossed thin strips of wood or other material, commonly used as a garden trellis.
- (group theory) A discrete subgroup of Rⁿ which is isomorphic to Zⁿ (considered as an additive group) and which spans the real vector space Rⁿ.
- an arrangement of points or particles or objects in a regular periodic pattern in 2 or 3 dimensions
- framework consisting of an ornamental design made of strips of wood or metal
- small opening (like a window in a door) through which business can be transacted
verb
noun
- (algebra, ring theory) An invariant of rings and modules, encoding information about dimensionality; see Depth (ring theory).
- the most severe part
- the vertical distance below a surface; the degree to which something is deep
- (statistics) the lower of the two ranks of a value in an ordered set of values
- lowness
- (literary, usually in the plural) the deepest part (usually of a body of water)
- (logic) the number of simple elements which an abstract conception or notion includes; the comprehension or content
- the distance between the front and the back, as the depth of a drawer or closet
- (horology) a pair of toothed wheels which work together
- (art, photography) the property of appearing three-dimensional
- (cryptography) A set of more than one ciphertext enciphered with the same key.
- (computing, colors) the total palette of available colors
- (aeronautics) the perpendicular distance from the chord to the farthest point of an arched surface
- (figuratively) the intensity, complexity, strength, seriousness or importance of an emotion, situation, etc.
- (literary, usually in the plural) a very remote part.
- (usually plural) a low moral state
- the attribute or quality of being deep, strong, or intense
- degree of psychological or intellectual profundity
- the intellectual ability to penetrate deeply into ideas
- the extent downward or backward or inward
noun
- (algebra, ring theory) An algebraic structure similar to a ring, but without the requirement that every element have an additive inverse.
- A promiscuous woman.
- (slang) Equipment used for taking recreational drugs.
- (slang, computing) A personal computer, typically one modified for looks.
- The special apparatus used for drilling wells.
- (US) A large truck, especially a semi-trailer truck.
- (slang) Radio equipment, especially a citizen's band transceiver.
- (nautical) The rigging of a sailing ship or other such craft.
- An imperfectly castrated horse, sheep etc.
- (informal) A costume or an outfit.
- (Northern England, Scotland, dialect) A ridge.
- Special equipment or gear used for a particular purpose.
- (animation) A model outfitted with parameterized controls for animation.
- a set of clothing (with accessories)
- gear used in fishing
- formation of masts, spars, sails, etc., on a vessel
- the act of swindling by some fraudulent scheme
- a truck consisting of a tractor and trailer together
- gear (including necessary machinery) for a particular enterprise
- a vehicle with wheels drawn by one or more horses
verb
- (transitive, intransitive, animation) To outfit a model with controls for animation.
- (transitive, manufacturing) To move (a heavy object) with the help of slings, hoists, block and tackle, levers, or similar equipment.
- (transitive) To manipulate something dishonestly for personal gain or discriminatory purposes.
- (transitive) To make or construct something in haste or in a makeshift manner.
- (transitive, informal) To dress or clothe in some costume.
- (transitive, nautical) To equip and fit (a ship) with sails, shrouds, and yards.
- equip with sails or masts
- manipulate in a fraudulent manner
- connect or secure to
- arrange the outcome of by means of deceit
noun
- (commutative algebra, of a module M over a commutative ring R) The set of all prime ideals of R such that the localization of M at the prime is nonzero, denoted operatorname SuppM
- (sometimes attributive) Something which supports.
- An accompaniment in music.
- Evidence.
- (fuzzy set theory) A set whose elements are at least partially included in a given fuzzy set (i.e., whose grade of membership in that fuzzy set is strictly greater than zero).
- (mathematics) in relation to a function, the set of points where the function is not zero; the closure of that set.
- (structural analysis) Horizontal, vertical or rotational support of structures: movable, hinged, fixed.
- An actor playing a subordinate part with a star.
- (computing) Compatibility and functionality for a given product or feature.
- Answers to questions and resolution of problems regarding something sold.
- Financial or other help.
- (gymnastics) Clipping of support position.
- financial resources provided to make some project possible
- any device that bears the weight of another thing
- the act of bearing the weight of or strengthening
- supporting structure that holds up or provides a foundation
- a military operation (often involving new supplies of men and materiel) to strengthen a military force or aid in the performance of its mission
- aiding the cause or policy or interests of
- the activity of providing for or maintaining by supplying with money or necessities
- something providing immaterial assistance to a person or cause or interest
- the financial means whereby one lives
- a musical part (vocal or instrumental) that supports or provides background for other musical parts
- documentary validation
verb
- (transitive) To answer questions and resolve problems regarding something sold.
- (transitive) To serve, as in a customer-oriented position; to give support to.
- (transitive) To provide evidence for; to lend credibility to.
- (transitive) To provide sustenance or maintenance for; to sustain in integrity or livelihood.
- (transitive) To back or favor a cause, party, etc., mentally or with concrete aid:
- (transitive) To help keep from falling.
- (transitive) To play a lesser part in the same production with (a star performer).
- (transitive) To assist or be involved with, but not be responsible for.
- (transitive) To help, particularly financially; to subsidize.
- (transitive, said of electronic devices, programming languages, etc.) To be designed to provide capacity for; to work or be compatible with (a part, accessory, file type, program, algorithm, etc.).
- be the physical support of; carry the weight of
- be a regular customer or client of
- put up with something or somebody unpleasant
- argue or speak in defense of
- support with evidence or authority or make more certain or confirm
- adopt as a belief
- give moral or psychological support, aid, or courage to
- establish or strengthen as with new evidence or facts
- play a subordinate role to (another performer)
- be behind; approve of
- support materially or financially
noun
- An algebraic structure consisting of a module over a commutative ring (or a vector space over a field) along with an additional binary operation that is bilinear over module (or vector) addition and scalar multiplication.
- (figurative) A system or process (especially one that is complex or convoluted) that substitutes one thing for another, or uses signs or symbols to represent concepts or ideas.
- (countable, set theory, mathematical analysis) A collection of subsets of a given set, such that this collection contains the empty set, and the collection is closed under unions and complements (and thereby also under intersections and differences).
- (uncountable, mathematics, sometimes capitalized) Abstract algebra: A broad field of study in modern mathematics (often mentioned alongside analysis) loosely characterized by its concern for abstraction and symmetry, dealing with the behavior, classification, and application of a large class of objects (called algebraic structures) and the maps between them (called, most generally, morphisms).
- (uncountable, medicine, historical, rare) The surgical treatment of a dislocated or fractured bone. Also (countable): a dislocation or fracture.
- (uncountable, mathematics) Elementary algebra: A system for representing and manipulating unknown quantities (variables) in equations.
- A universal algebra.
- the mathematics of generalized arithmetical operations
noun
- (algebra) A ring of fractions of a given ring, such that the complement of the set of allowed denominators is an ideal.
- (algebra) A systematic method of adding multiplicative inverses to a ring.
- (software engineering) The act, process, or result of making a product suitable for use in a particular country or region.
- (translation studies, chiefly software, marketing) The act, process, or result of adapting translated text to fit a local culture; domestication.
- The act of localizing.
- (Hong Kong politics, specifically) The switch of positions in power from the colonizing population to the local population.
- The state of being localized.
- (physiology) the principle that specific functions have relatively circumscribed locations in some particular part or organ of the body
- a determination of the place where something is
noun
- (algebra, ring theory) Initialism of central simple algebra.
- (countable) Initialism of community service announcement.
- (uncountable) Initialism of child sexual abuse.
- (US) Initialism of combined statistical area.
- (algebra, Lie theory) Initialism of Cartan subalgebra.
- (uncountable) Initialism of community-supported agriculture.
name
- (Northern Ireland) Initialism of Central Services Agency.
- (British) Initialism of Child Support Agency.
- (Canada, space flight) Initialism of Canadian Space Agency.
- (Canada) Initialism of Canadian Standards Association.
- (US) Initialism of Confederate States of America.
- (US) Initialism of Controlled Substances Act.
noun
- (mathematics, algebra) The additive identity element of a monoid or greater algebraic structure, particularly a group or ring.
- (mathematics) A value of the independent variables of a function, for which the function is equal to zero.
- The value of a magnitude corresponding to the cardinal number zero.
- (informal, uncountable) Nothing, or none.
- The numeric symbol that represents the cardinal number zero.
- The point on a scale at which numbering or measurement originates.
- (slang) A person dismissed as unimportant.
- (finance) A security which has a zero coupon (paying no periodic interest).
- The digit 0 in the decimal, binary, and all other base numbering systems.
- (military, usually capitalized) A Mitsubishi A6M Zero, a long range fighter aircraft operated by the Imperial Japanese Navy Air Service from 1940 to 1945.
- A setting of calibrated instruments such as a firearm, corresponding to a zero value.
- a quantity of no importance; thing (object:), singular, negative pronoun; pronoun, thing, singular; quantifier: negative existential
- the point on a scale from which positive or negative numerical quantities can be measured
- the sight setting that will cause a projectile to hit the center of the target with no wind blowing
- a mathematical element that when added to another number yields the same number
adj
- (meteorology) Of a cloud ceiling, limiting vision to 50 feet (15 meters) or less.
- (linguistics) Present at an abstract level, but not realized in the surface form.
- (meteorology) Of horizontal visibility, limited to 165 feet (50.3 meters) or less.
- (postpositive) Used in the names of foodstuffs, especially beverages, to indicate a version with no calories
- of or relating to the null set (a set with no members)
- having no measurable or otherwise determinable value
- indicating the absence of any or all units under consideration
- indicating an initial point or origin
det
num
verb
noun
- (mathematics, linear algebra) A relation between generators of a module.
- (Jungian psychology) An archetypal pairing of contrasexual opposites, symbolizing the communication of the conscious and unconscious minds.
- (astronomy, astrology) An alignment of three celestial bodies (for example, the Sun, Earth, and Moon) such that one body is directly between the other two, such as occurs at an eclipse.
- (zoology) The association of two protozoa end-to-end or laterally for the purpose of asexual exchange of genetic material.
- (Gnosticism) Complementary female–male pairings of the emanations known as Aeons.
- (genetics) The pairing of chromosomes in meiosis.
- (medicine) The fusion of some or all of the organs.
- the straight line configuration of 3 celestial bodies (as the sun and earth and moon) in a gravitational system
noun
- (algebra, ring theory) A two-sided ideal; a subset of a ring which is closed under both left and right multiplication by elements of the ring.
- (algebra) A subsemigroup with the property that if any semigroup element outside of it is added to any one of its members, the result must lie outside of it.
- (algebra, order theory, lattice theory) A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).
- A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
- (algebra, Lie theory) A Lie subalgebra (subspace that is closed under the Lie bracket) 𝖍 of a given Lie algebra 𝖌 such that the Lie bracket [𝖌,𝖍] is a subset of 𝖍.
- (set theory) A collection of sets, considered small or negligible, such that every subset of each member and the union of any two members are also members of the collection.
- model of excellence or perfection of a kind; one having no equal
- the idea of something that is perfect; something that one hopes to attain
adj
- Existing only in the mind; conceptual, imaginary.
- Optimal; being the best possibility.
- Teaching or relating to the doctrine of idealism.
- Pertaining to ideas, or to a given idea.
- Perfect, flawless, having no defects.
- (mathematics) Not actually present, but considered as present when limits at infinity are included.
- of or relating to the philosophical doctrine of the reality of ideas
- conforming to an ultimate standard of perfection or excellence; embodying an ideal
- constituting or existing only in the form of an idea or mental image or conception
noun
- (algebra, somewhat humorous) An associated prime of a module.
- Someone who intentionally kills a person, especially a professional who kills a public or political figure.
- (historical, usually capitalized) A member of the Nizari Ismaili Muslim community of the Alamut Period.
- Any ruthless killer.
- a murderer (especially one who kills a prominent political figure) who kills by a surprise attack and often is hired to do the deed
- a member of a secret order of Muslims (founded in the 12th century) who terrorized and killed Christian Crusaders
verb
noun
- (algebra, group theory, ring theory) The set of those elements (of a given algebraic structure) that commute with every other element, usually denoted Z(G). In the case of (semi-)groups, it is required that they commute under the (semi-)group operation; in the case of rings and (Lie) algebras, under multiplication (i.e. the bracket for Lie algebras)
- A place, especially a building or complex, set aside for some specified function or activity.
- (engineering) A conical recess or indentation in the end of a shaft or other work, to receive the point of a center, on which the work can turn, as in a lathe.
- (American football, Canadian football) The person who holds the ball at the beginning of each play.
- (geometry) The point in the interior of any figure of any number of dimensions that has as its coordinates the arithmetic mean of the coordinates of all points on the perimeter of the figure (or of all points in the interior for a center of volume).
- (basketball) The player, generally the tallest, who plays closest to the basket.
- (ice hockey) The forward that generally plays between the left wing and right wing and usually takes the faceoffs.
- (geometry) A point on a triangle's plane that is in some sense in its middle.
- The point in the interior of a sphere that is equidistant from all points on the circumference.
- The point in the interior of a circle that is equidistant from all points on the circumference.
- The middle portion of something; the part well away from the edges.
- (netball) A player who can go all over the court, except the shooting circles.
- (Australia, New Zealand) The ring in the gambling game two-up in which the spinner operates.
- (soccer) A pass played into the centre of the pitch.
- (rugby) One of the backs operating in a central area of the pitch, either the inside centre or outside centre.
- A topic that is particularly important in a given context, the element in a subject of cognition, volition or discussion that is perceived as decisive.
- (geometry) The point on a line that is midway between the ends.
- (engineering) One of the two conical steel pins in a lathe, etc., upon which the work is held, and about which it revolves.
- The venue in which the head of government in a centralized state is situated.
- (politics) The ensemble of moderate or centrist political parties.
- (architecture) A temporary structure upon which the materials of a vault or arch are supported in position until the work becomes self-supporting.
- (ice hockey) the person who plays center on a hockey team
- politically moderate persons; centrists
- the position on a hockey team of the player who participates in the face off at the beginning of the game
- (football) the person who plays center on the line of scrimmage and snaps the ball to the quarterback
- mercantile establishment consisting of a carefully landscaped complex of shops representing leading merchandisers; usually includes restaurants and a convenient parking area; a modern version of the traditional marketplace
- a place where some particular activity is concentrated
- the middle of a military or naval formation
- a position on a basketball team of the player who participates in the jump that starts the game
- the piece of ground in the outfield directly ahead of the catcher
- the object upon which interest and attention focuses
- (American football) the position of the player on the line of scrimmage who puts the ball in play
- a point equidistant from the ends of a line or the extremities of a figure
- (basketball) the person who plays center on a basketball team
- the choicest or most essential or most vital part of some idea or experience
- a building dedicated to a particular activity
- an area that is approximately central within some larger region
- a cluster of nerve cells governing a specific bodily process
- the sweet central portion of a piece of candy that is enclosed in chocolate or some other covering
adj
verb
- (transitive) To give (something) a central basis.
- (intransitive) To concentrate on (something), to pay close attention to (something).
- (transitive) To cause (some attribute, such as a mood or voltage) to be adjusted to a value which is midway between the extremes.
- (transitive) To cause (an object) to occupy the center of an area.
- (engineering) To form a recess or indentation for the reception of a center.
- direct one's attention on something
- center upon
- move into the center
noun
- (algebraic topology, homological algebra, more generally) An element of a group (or module) in a chain complex.
- A livery collar, a chain of office.
- A unit of length, exactly equal to 22 yards, which is 4 rods or 100 links, and approximately equal to 20.12 metres; the length of a Gunter's surveying chain; the length of a cricket pitch.
- That which confines, fetters, or secures; a bond.
- A series of stores or businesses with the same brand name.
- A series of interconnected things.
- (weaving) The warp threads of a web.
- (British) A sequence of linked house purchases, each of which is dependent on the preceding and succeeding purchase (said to be "broken" if a buyer or seller pulls out).
- (surveying) A series of interconnected links of known length, used as a measuring device.
- A series of interconnected rings or links usually made of metal.
- (surveying) A long measuring tape.
- (mathematics, set theory, order theory) A totally ordered set, especially a totally ordered subset of a poset.
- (nautical, in the plural) Iron links bolted to the side of a vessel to bold the dead-eyes connected with the shrouds; also, the channels.
- (algebraic topology, originally) A formal sum of cells in a CW complex of a certain dimension k (in which case the formal sums are called k'''-chains); a formal sum of simplices or cubes of a certain dimension in a simplical complex or cubical complex (respectively).
- (organic chemistry, physical chemistry) A number of atoms in a series, which combine to form a molecule.
- a unit of length
- a series of things depending on each other as if linked together
- (chemistry) a series of linked atoms (generally in an organic molecule)
- anything that acts as a restraint
- a series of (usually metal) rings or links fitted into one another to make a flexible ligament
- a necklace made by stringing objects together
- a linked or connected series of objects
- (business) a number of similar establishments (stores or restaurants or banks or hotels or theaters) under one ownership
- a series of hills or mountains
verb
- (computing) To be chained to another data item.
- (transitive, computing, rare, associated with Acorn Computers) To load and automatically run (a program).
- (intransitive) To link multiple items together.
- (figurative) To connect as if with a chain, due to dependence, addiction, or other feelings
- (computing) To relate data items with a chain of pointers.
- (transitive) To measure a distance using a 66-foot long chain, as in land surveying.
- (figurative) To obligate.
- (transitive) To secure someone with fetters.
- (transitive) To fasten something with a chain.
- (transitive) To obstruct the mouth of a river etc with a chain.
- fasten or secure with chains
- connect or arrange into a chain by linking
verb
- (generally, of an algebraic structure) To be expressable as a direct sum of sub-modules, -algebras, etc.
- (algebra, transitive and intransitive, acts on a polynomial) To factor into linear factors.
- (transitive, intransitive, slang) To leave.
- (sports, especially baseball) For both teams involved in a doubleheader to win one game each and lose another.
- (intransitive, of a couple) To separate.
- (of an object which expresses the relationship between algebraic structures, particularly a short exact sequence) To contain an object which may be so expressed.
- (transitive) To share; to divide.
- To be broken; to be dashed to pieces.
- (ambitransitive) To (cause to) break up; to throw into discord.
- (intransitive, of something solid, particularly wood) To break along the grain fully or partly along a more or less straight line.
- (intransitive) To burst out laughing.
- (transitive, ergative, of something solid) To divide fully or partly along a more or less straight line.
- (intransitive, politics) To vote for candidates of opposite parties.
- come open suddenly and violently, as if from internal pressure
- discontinue an association or relation; go different ways
- go one's own way; move apart
- separate or cut with a tool, such as a sharp instrument
- separate into parts or portions
adj
- (algebra, of a short exact sequence) Having the middle object (group, module, etc.) equal to the direct sum of the others.
- (stock exchange, historical, of quotations) Given in sixteenths rather than eighths.
- (London stock exchange) Designating ordinary stock that has been divided into preferred ordinary and deferred ordinary.
- Divided.
- (of coffee) Comprising half decaffeinated and half caffeinated espresso.
- (stock exchange, of an order, sale, etc.) Divided so as to be done or executed part at one time or price and part at another time or price.
- (especially of wood) cut or ripped longitudinally with the grain
- having been divided; having the unity destroyed
noun
- A crack or longitudinal fissure.
- A dessert or confection resembling a banana split.
- (bowling) A result of a first throw that leaves two or more pins standing with one or more pins between them knocked down.
- (baseball, slang) A split-finger fastball.
- A bottle of wine containing 37.5 centiliters, half the volume of a standard 75-centiliter bottle; a demi.
- (bodybuilding) A workout routine as seen by its distribution of muscle groups or the extent and manner they are targeted in a microcycle.
- A breach or separation, as in a political party; a division.
- A unit of measure used for champagne or other spirits: 18.75 centiliters or one quarter of a standard 75-centiliter bottle. Commercially comparable to ¹⁄₂₀ (US) gallon, which is ¹⁄₂ of a fifth.
- (gymnastics, cheerleading, dance, usually in the phrase "to do the splits") A maneuver of spreading or sliding the feet apart until the legs are flat on the floor 180 degrees apart, either sideways to the body or with one leg in front and one behind, thus lowering the body completely to the floor in an upright position.
- (systematics) The division of a single taxon into two or more taxa; as opposed to a lump.
- A piece that is split off, or made thin, by splitting; a splinter; a fragment.
- (construction) A tear resulting from tensile stresses.
- (music) A recording containing songs by multiple artists; a split single or split album.
- (gambling) A division of a stake happening when two cards of the kind on which the stake is laid are dealt in the same turn.
- A split shot or split stroke.
- (athletics, speedrunning) The elapsed time at specific intermediate points in a race or speedrun.
- (leather manufacture) One of the sections of a skin made by dividing it into two or more thicknesses.
- a promised or claimed share of loot or money
- a dessert of sliced fruit and ice cream covered with whipped cream and cherries and nuts
- (tenpin bowling) a divided formation of pins left standing after the first bowl
- a lengthwise crack in wood
- a bottle containing half the usual amount
- the act of rending or ripping or splitting something
- extending the legs at right angles to the trunk (one in front and the other in back)
- an increase in the number of outstanding shares of a corporation without changing the shareholders' equity
- an opening made forcibly as by pulling apart
- division of a group into opposing factions
adv
- (algebra) Of a subgroup of finite index.
- By computer or in cyberspace.
- (topology) Of a covering space of finite degree.
- Almost but not quite.
- In essence or functionally, but not in fact, formally, or technically.
- in essence or effect but not in fact
- (of actions or states) slightly short of or not quite accomplished; all but
adj
- (mathematics) Of a ring: such that all submodules of projective modules over the ring are also projective.
- Of a person: holding a legally hereditary title or rank.
- Of a title, honor or right: legally granted to somebody's descendant after that person's death.
- Passed on as an inheritance, by last will or intestate.
- Of a disease or trait: passed from a parent to offspring in the genes.
- occurring among members of a family usually by heredity
- inherited or inheritable by established rules (usually legal rules) of descent
noun
adj
- (ring theory, of a module (or algebra) over a ring) finitely generated (as a module).
- (grammar) Limited by (i.e. inflected for) person or number.
- Having an end or limit; (of a quantity) constrained by bounds; (of a set) whose number of elements is a natural number.
- bounded or limited in magnitude or spatial or temporal extent
- (of verbs) relating to forms of the verb that are limited in time by a tense and (usually) show agreement with number and person
noun
adj
- (ring theory, of an algebra or ring) Semisimple as a module over itself; equivalently, such that all (left) modules are semisimple.
- (module theory, of a module) In which each submodule is a direct summand; equivalently, equal to a direct sum of simple submodules.
- (representation theory, of a linear representation of a group or algebra) Being a direct sum of simple representations (also known as irreducible representations).
- (category theory, most generally, of an abelian category) Containing a collection of simple objects such that all objects in the category are direct sums of these simple objects.
- (Lie theory, of a Lie algebra) Being a direct sum of simple Lie algebras.
- (linear algebra, of an operator or matrix) For which every invariant subspace has an invariant complement, equivalent to the minimal polynomial being squarefree.
- (group theory, of an algebraic group) Being a linear algebraic group whose radical of the identity component is trivial.
- (of a ring, somewhat proscribed) Semiprimitive: having trivial Jacobson radical.
adj
- (algebra, of a module) Finitely generated and such that all finitely generated submodules are finitely presented.
- (algebra, of a ring) Such that every finitely generated (left) ideal is finitely presented.
- Aesthetically ordered.
- Having a natural or due agreement of parts; harmonious: a coherent design.
- (mathematics, sheaf theory, of a sheaf) Belonging to a specific class of sheaves having particularly manageable properties closely linked to the geometrical properties of the underlying space. See Coherent sheaf on Wikipedia.Wikipedia
- Orderly, logical and consistent.
- Unified; sticking together; making up a whole.
- (botany) Attaching or pressing against an organ of the same nature.
- (topology, of a topology 𝒯 on a set T with respect to a family C_a of subsets of T) In a technical sense, determined by the (topology of) the subsets. Formally, Such that 𝒯 is the finest topology on T for which the inclusion maps ιₐ:C_a→T are continuous, where each C_a is considered with its subspace topology.
- (physics) Of waves having the same direction, wavelength and phase, as light in a laser.
- marked by an orderly, logical, and aesthetically consistent relation of parts
- (physics) of waves having a constant phase relation
- sticking together
- capable of thinking and expressing yourself in a clear and consistent manner
adj
- (algebra, of a ring) Having a unique maximal (left) ideal.
- (group theory, of a property of an infinite group) Satisfied by every finitely generated subgroup.
- (topology) Satisfied by at least one open neighborhood of every point.
- (computing, of a resource) Connected directly to a particular computer, processor, etc.; able to be accessed offline.
- (topology) Satisfied by arbitrarily small open neighborhoods of every point.
- (group theory, of a property of a finite group) Detectable from the behavior of the normalizers of the nontrivial p-subgroups.
- (algebra, algebraic geometry, of a property P of a ring R (or an R-module M)) Such that the following conditions are equivalent: (1) P holds for R (M); (2) P holds for the localization R_p (M_p) for all prime ideals p of R; (3) P holds for the localization R_m (M_m) for all maximal ideals m of R.
- (medicine) Of or pertaining to a restricted part of an organism.
- From or in a nearby location.
- (computing, of a variable or identifier) Having limited scope (either lexical or dynamic); only accessible within a certain portion of a program.
- Descended from an indigenous population.
- affecting only a restricted part or area of the body
- of or belonging to or characteristic of a particular locality or neighborhood
- relating to or applicable to or concerned with the administration of a city or town or district rather than a larger area
adv
noun
- (colloquial, medicine) Clipping of local anesthetic.
- (programming) A locally scoped identifier.
- A person who lives in or near a given place.
- (rail transport) Clipping of local train.
- A branch of a nationwide organization such as a trade union.
- (British) One's nearest or regularly frequented public house or bar.
- (fandom slang, derogatory) A Twitter user who is not a part of Stan Twitter.
- (finance) An independent trader who acts for themselves rather than on behalf of investors.
- (US, slang, journalism) An item of news relating to the place where the newspaper is published.
- public transport consisting of a bus or train that stops at all stations or stops
- anesthetic that numbs a particular area of the body
adj
- (commutative algebra, of a module M over a noetherian ring) Such that all localizations of M at maximal ideals contained in the support of M are either Cohen-Macaulay or trivial.
- (commutative algebra, of a noetherian local ring) Cohen-Macaulay as a module over itself.
- (commutative algebra, of a finite module over a noetherian local ring) Such that its depth is equal to its Krull dimension.
- (commutative algebra, of a noetherian ring) Cohen-Macaulay as a module over itself.
adj
- (module theory, of a module) Being non-trivial, and having no proper non-trivial submodules (equivalently, no proper non-trivial quotient modules).
- Uncomplicated; lacking complexity; taken by itself, with nothing added.
- Free from duplicity; guileless, innocent, straightforward.
- (botany) Not compound, but possibly lobed.
- Easy; not difficult.
- (now colloquial, euphemistic) Feeble-minded; foolish.
- (zoology) Consisting of a single individual or zooid; not compound.
- (algebra, of a Lie algebra) Being non-abelian and having no proper non-zero ideals. (Note that this is non-equivalent to the usual algebra sense; in particular, the abelian Lie algebra of dimension 1 over any given field is non-trivial and has no proper non-zero ideals, but is by convention not considered simple.)
- (mineralogy) Homogenous.
- (ring theory, of a ring) Being non-zero, and having no proper non-zero two-sided ideals (equivalently, no proper non-trivial quotient rings). For commutative rings, this definition coincides with that of a field.
- Without ornamentation; plain.
- (mathematics, real analysis, measure theory, of a real-valued function) Equal to a finite linear combination of indicator functions on measurable sets.
- (group theory, of a group) Being non-trivial, and having no proper non-trivial normal subgroups (equivalently, no proper non-trivial quotient groups).
- Undistinguished in social condition; of no special rank.
- (category theory, of an object in a category with a terminal object) Being non-isomorphic to the terminal object, and such that its only quotient objects (up to isomorphism) are the terminal object and itself.
- (chemistry, pharmacology) Consisting of one single substance; uncompounded.
- Using steam only once in its cylinders, in contrast to a compound engine, where steam is used more than once in high-pressure and low-pressure cylinders. (of a steam engine)
- (universal algebra, of an algebraic structure) Containing more than one element, and such that the only congruences on the structure are the diagonal relation (the equivalence relation a≡b⟺a=b) and the universal relation (the equivalence relation such that a≡b for all a,b). Equivalently, containing more than one element and having no proper non-trivial quotient algebras.
- exhibiting childlike simplicity and credulity
- (botany) of leaf shapes; of leaves having no divisions or subdivisions
- having few parts; not complex or complicated or involved
- apart from anything else; without additions or modifications
- easy and not involved or complicated
- lacking mental capacity and subtlety
- unornamented
noun
- (weaving) A drawloom.
- (logic) A simple or atomic proposition.
- (pharmacology) A herbal preparation made from one plant, as opposed to something made from more than one plant.
- (Roman Catholicism) A feast which is not a double or a semidouble.
- (weaving) Part of the apparatus for raising the heddles of a drawloom.
- a person lacking intelligence or common sense
- any herbaceous plant having medicinal properties
verb
- (generally, of an algebraic structure) To be expressable as a direct sum of sub-modules, -algebras, etc.
- (algebra, transitive and intransitive, acts on a polynomial) To factor into linear factors.
- (transitive, intransitive, slang) To leave.
- (sports, especially baseball) For both teams involved in a doubleheader to win one game each and lose another.
- (intransitive, of a couple) To separate.
- (of an object which expresses the relationship between algebraic structures, particularly a short exact sequence) To contain an object which may be so expressed.
- (transitive) To share; to divide.
- To be broken; to be dashed to pieces.
- (ambitransitive) To (cause to) break up; to throw into discord.
- (intransitive, of something solid, particularly wood) To break along the grain fully or partly along a more or less straight line.
- (intransitive) To burst out laughing.
- (transitive, ergative, of something solid) To divide fully or partly along a more or less straight line.
- (intransitive, politics) To vote for candidates of opposite parties.
- come open suddenly and violently, as if from internal pressure
- discontinue an association or relation; go different ways
- go one's own way; move apart
- separate or cut with a tool, such as a sharp instrument
- separate into parts or portions
adj
- (algebra, of a short exact sequence) Having the middle object (group, module, etc.) equal to the direct sum of the others.
- (stock exchange, historical, of quotations) Given in sixteenths rather than eighths.
- (London stock exchange) Designating ordinary stock that has been divided into preferred ordinary and deferred ordinary.
- Divided.
- (of coffee) Comprising half decaffeinated and half caffeinated espresso.
- (stock exchange, of an order, sale, etc.) Divided so as to be done or executed part at one time or price and part at another time or price.
- (especially of wood) cut or ripped longitudinally with the grain
- having been divided; having the unity destroyed
noun
- A crack or longitudinal fissure.
- A dessert or confection resembling a banana split.
- (bowling) A result of a first throw that leaves two or more pins standing with one or more pins between them knocked down.
- (baseball, slang) A split-finger fastball.
- A bottle of wine containing 37.5 centiliters, half the volume of a standard 75-centiliter bottle; a demi.
- (bodybuilding) A workout routine as seen by its distribution of muscle groups or the extent and manner they are targeted in a microcycle.
- A breach or separation, as in a political party; a division.
- A unit of measure used for champagne or other spirits: 18.75 centiliters or one quarter of a standard 75-centiliter bottle. Commercially comparable to ¹⁄₂₀ (US) gallon, which is ¹⁄₂ of a fifth.
- (gymnastics, cheerleading, dance, usually in the phrase "to do the splits") A maneuver of spreading or sliding the feet apart until the legs are flat on the floor 180 degrees apart, either sideways to the body or with one leg in front and one behind, thus lowering the body completely to the floor in an upright position.
- (systematics) The division of a single taxon into two or more taxa; as opposed to a lump.
- A piece that is split off, or made thin, by splitting; a splinter; a fragment.
- (construction) A tear resulting from tensile stresses.
- (music) A recording containing songs by multiple artists; a split single or split album.
- (gambling) A division of a stake happening when two cards of the kind on which the stake is laid are dealt in the same turn.
- A split shot or split stroke.
- (athletics, speedrunning) The elapsed time at specific intermediate points in a race or speedrun.
- (leather manufacture) One of the sections of a skin made by dividing it into two or more thicknesses.
- a promised or claimed share of loot or money
- a dessert of sliced fruit and ice cream covered with whipped cream and cherries and nuts
- (tenpin bowling) a divided formation of pins left standing after the first bowl
- a lengthwise crack in wood
- a bottle containing half the usual amount
- the act of rending or ripping or splitting something
- extending the legs at right angles to the trunk (one in front and the other in back)
- an increase in the number of outstanding shares of a corporation without changing the shareholders' equity
- an opening made forcibly as by pulling apart
- division of a group into opposing factions
adj
- (algebra, ring theory, of a ring homomorphism) Such that its target, regarded as a module over its source, is flat (as above).
- (not comparable, commerce) Of fees, fares etc., fixed; unvarying.
- Smooth; having no protrusions, indentations or other surface irregularities, or relatively so.
- (golf, of a golf club) Having a head at a very obtuse angle to the shaft.
- At a consistently depressed level; consistently lacklustre.
- (of colours) Without variation in tone or hue (uniform), and dull (not glossy).
- (music, note) Lowered by one semitone.
- In a horizontal line or plane; not sloping.
- (juggling, of a throw) Without spin; spinless.
- (algebraic geometry, scheme theory, of a morphism of schemes) Such that the induced map on every stalk is flat (as a map of rings).
- (authorship, figuratively, especially of a character) Lacking in depth, substance, or believability; underdeveloped; one-dimensional.
- (horticulture, of certain fruits) Flattening at the ends.
- (slang) Having small or invisible breasts and/or buttocks.
- (phonetics, of a vowel) Not diphthongal; without variation in height or backness.
- (of a tire or other inflated object) Deflated, especially because of a puncture.
- (homological algebra, of a module) Such that the tensor product preserves exact sequences. See Flat module on Wikipedia.Wikipedia.
- (of a battery) Unable to emit power; dead.
- (of measurements of time) Exact.
- Without variation in level, quantity, value, tone etc.
- Having no variations in height.
- (music) Of a note or voice, lower in pitch than it should be.
- (music, voice) Without variations in pitch.
- (figurative) Lacking liveliness or action; depressed; uninteresting; dull and boring.
- Absolute; downright; peremptory.
- (grammar) Not having an inflectional ending or sign, such as a noun used as an adjective, or an adjective as an adverb, without the addition of a formative suffix; or an infinitive without the sign "to".
- (wine) Lacking acidity without being sweet.
- (of coffee) Having little froth and little milk.
- (of a carbonated drink) With all or most of its carbon dioxide having come out of solution so that the drink no longer fizzes or contains any bubbles.
- sounded or spoken in a tone unvarying in pitch
- not reflecting light; not glossy
- having lost effervescence
- lacking contrast or shading between tones
- horizontally level
- stretched out and lying at full length along the ground
- having a relatively broad surface in relation to depth or thickness
- lacking taste or flavor or tang
- flattened laterally along the whole length (e.g., certain leafstalks or flatfishes)
- not modified or restricted by reservations
- commercially inactive
- lacking stimulating characteristics; uninteresting
- having a surface without slope, tilt in which no part is higher or lower than another
- (of a musical note) lowered in pitch by one chromatic semitone
- lacking the expected range or depth; not designed to give an illusion or depth
adv
- Completely, firmly, or unequivocally.
- Directly; flatly.
- (with units of time, distance, etc) Used to emphasize the smallness of the measurement.
- (finance, slang) Without allowance for accrued interest.
- Completely.
- (of accurately measured timings) Exactly, precisely.
- So as to be flat.
- (of a sentence) Without parole.
- with flat sails
- in a forthright manner; candidly or frankly
noun
- (American football) The areas behind the line of scrimmage to either side of an offensive football formation.
- (rail transport) A flat spot on the wheel of a rail vehicle.
- (publishing) A flat, glossy children's book with few pages.
- An area of level ground (sometimes covered with shallow or tidal water).
- (technical, theatre, stagecraft) A rectangular wooden structure covered with masonite, lauan, or muslin, often produced in standard modules, that is used to build wall surfaces on stage. Flats can be painted and outfitted with doors and/or windows to depict a building or other part of a scene, and are a hard-surfaced alternative to a backcloth or backdrop.
- (entomology) Any of various hesperiid butterflies that spread their wings open when they land.
- A flat sheet for use on a bed.
- (horse racing, with 'the' or attributively, sometimes with capital) Level horse-racing ground, as contrasted with courses incorporating jumps, or the racing done on such ground.
- (postal) A large mail piece measuring at least 8 1/2 by 11 inches, such as catalogs, magazines, and unfolded paper enclosed in large envelopes.
- (music) A note played one chromatic semitone lower than a natural, denoted by the symbol ♭ placed after the letter representing the note (e.g., B♭) or in front of the note symbol (e.g. ♭♪).
- (in the plural) A type of ladies' shoe with a very low heel.
- (informal, automotive) A flat tyre/flat tire.
- (painting) A thin, broad brush used in oil and watercolour painting.
- (optics) A flat (i.e. plane) mirror
- Ellipsis of flat ride (“spinning amusement ride”).
- A wide, shallow container or pallet.
- (geometry) A subset of n-dimensional space that is congruent to a Euclidean space of lower dimension.
- (in the plural) A type of flat-soled running shoe without spikes.
- The most prominent flat part of something.
- A flat-bottomed boat, without keel, and of small draught.
- (swordfighting) The flat side of a blade, as opposed to the sharp edge.
- A straw hat, broad-brimmed and low-crowned.
- A platform on a wheel, upon which emblematic designs etc. are carried in processions.
- (Australia, horse racing, with 'the' or attributively, sometimes with capital) the area in the centre of a racecourse.
- (gambling, slang) A cheater's die with the edges shaved to make certain rolls more likely.
- (in the phrase 'the flat') Level ground in general.
- (historical) An early kind of toy soldier having a flat design.
- (US) Ellipsis of flat water (“nonfizzy drinking water”).
- (chiefly British, New England, South Africa, India, Australia, New Zealand, Singapore, archaic elsewhere) A complete domicile occupying only part of a building, especially one for rent
- (Canadian Prairies, British Columbia) A 24-case of beer.
- The palm of the hand, with the adjacent part of the fingers.
- (rail transport, US) A railroad car without a roof, and whose body is a platform without sides; a platform car or flatcar.
- (mining) A horizontal vein or ore deposit auxiliary to a main vein; also, any horizontal portion of a vein not elsewhere horizontal.
- a shallow box in which seedlings are started
- a deflated pneumatic tire
- scenery consisting of a wooden frame covered with painted canvas; part of a stage setting
- a level tract of land
- a musical notation indicating one half step lower than the note named
- a suite of rooms usually on one floor of an apartment house
- freight car without permanent sides or roof
verb
- (transitive) To dash or throw
- (poker slang) To make a flat call; to call without raising.
- (intransitive) To become flat or flattened; to sink or fall to an even surface.
- (intransitive, music, colloquial) To fall from the pitch.
- (intransitive) To dash, rush
- (transitive, music) To depress in tone, as a musical note; especially, to lower in pitch by half a tone.
adj
- (commutative algebra, of a ring) Such that all of its localizations at prime ideals are integrally closed domains.
- (topology, of a topology or topological space) In which disjoint closed sets can be separated by disjoint neighborhoods.
- (linear algebra, of a matrix) Which commutes with its conjugate transpose.
- (complex analysis, of a family of continuous functions) Which is pre-compact.
- (commutative algebra, of a domain) Integrally closed: equal its own integral closure in its field of fractions.
- (functional analysis, of a Hilbert space operator) Which commutes with its adjoint.
- (probability theory, statistics, of a distribution, random variable, etc.) Which has a very specific bell curve shape; that is or has the qualities of a normal distribution.
- (physics, of a mode in an oscillating system) In which all parts of an object vibrate at the same frequency (a normal mode).
- (rail transport, of points) In the default position, set for the most frequently used route.
- (chemistry) Of, relating to, or being a solution containing one equivalent weight of solute per litre of solution.
- (category theory, of a category) Which contains only normal morphisms.
- (organic chemistry) Describing a straight chain isomer of an aliphatic hydrocarbon, or an aliphatic compound in which a substituent is in the 1- position of such a hydrocarbon.
- (fandom slang, sarcastic, with “about”) Fervently interested in a subject; obsessed.
- (algebraic geometry, of a variety or scheme) Such that the local ring at every point is an integrally closed domain.
- (category theory, of a morphism) Which is the kernel or cokernel of some morphism, respectively.
- (number theory, of a real number) In whose representation in a given base b ≥ 2, for every positive integer n, the bⁿ possible strings of n digits follow a uniform distribution.
- Usual, healthy; not sick or ill or unlike oneself.
- (set theory, of a function from the ordinals to the ordinals) Which is strictly monotonically increasing and continuous with respect to the order topology.
- (algebra, of a field extension of a field K) Which is the splitting field of a family of polynomials in K.
- (algebra, of a subgroup) With cosets which form a group.
- (education, of a school) Teaching teachers how to teach; teaching teachers the norms of education.
- According to norms or rules or to a regular pattern.
- (geometry) Perpendicular to a tangent of a curve or tangent plane of a surface.
- in accordance with scientific laws
- conforming with or constituting a norm or standard or level or type or social norm; not abnormal
- forming a right angle
- being approximately average or within certain limits in e.g. intelligence and development
noun
- (geometry, countable) A line or vector that is perpendicular to another line, surface, or plane.
- (medicine, countable) A person who is healthy, normal, as opposed to one who is morbid.
- (slang, countable) A person who is normal, who fits into mainstream society, as opposed to those who live alternative lifestyles.
- (countable, uncountable) The usual state.
- something regarded as a normative example
adj
- (algebra, module theory, of a (left) module M over a ring R) Loosely, having a certain generalizing property, abstracted from the study of ℚ as a ℤ-module. Formally, such that any short exact sequence of (left) R-modules beginning with M splits, or any of several equivalent statements: See Injective module.
- (homological algebra, of a resolution) Such that the objects (usually modules) involved in the resolution are injective (in the algebraic senses above).
- (mathematics) Of, relating to, or being an injection: such that each element of the image (or range) is associated with at most one element of the preimage (or domain); inverse-deterministic
- (category theory, most generally, of an object Q in a category C) Loosely, having a property analogous to that which characterizes injective modules (see above). Formally, such that, given a monomorphism f:X→Y in C, for every morphism g:X→Q there exists a morphism h:Y→Q such that h∘f=g; see Injective object.
adj
- (algebra, commutative algebra, of a ring element in a ring B relative to a subring A) Being the root of some monic polynomial in A.
- Constituting a whole together with other parts or factors; not omittable or removable.
- (mathematics) Relating to integration (“the process of finding the integral [noun] of a function”).
- (mathematics) Of, pertaining to, or being an integer.
- constituting the undiminished entirety; lacking nothing essential especially not damaged
- of or denoted by an integer
- existing as an essential constituent or characteristic
noun
- (mathematics) One of the two fundamental operations of calculus (the other being differentiation), whereby a function's displacement, area, volume, or other qualities arising from the study of infinitesimal change are quantified, usually defined as a limiting process on a sequence of partial sums. Denoted using a long s: ∫, or a variant thereof.
- (mathematics) A definite integral: the result of the application of such an operation onto a function and a suitable subset of the function's domain: either a number or positive or negative infinity. In the former case, the integral is said to be finite or to converge; in the latter, the integral is said to diverge. In notation, the domain of integration is indicated either below the sign, or, if it is an interval, with its endpoints as sub- and super-scripts, and the function being integrated forming part of the integrand (or, generally, differential form) appearing in front of the integral sign.
- (specifically) Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc.
- (mathematics) An indefinite integral: the result of the application of such an operation onto a function together with an indefinite domain, yielding a function; a function's antiderivative;
- the result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x)
adj
- (algebra, of a nonzero module) Such that the annihilator of any nonzero submodule is equal to the annihilator of the whole module.
- Early; blooming; being in the first stage.
- First in excellence, quality, or value.
- First in importance, degree, or rank.
- First in time, order, or sequence.
- (algebra, of an ideal) Having its complement closed under multiplication.
- Marked or distinguished by the prime symbol.
- (mathematics, technical) Such that if it divides a product, it divides one of the multiplicands.
- (mathematics, lay) Having exactly two integral factors: itself and unity (1 in the case of integers).
- used of the first or originating agent
- being at the best stage of development
- first in rank or degree
- of or relating to or being an integer that cannot be factored into other integers
- of superior grade
noun
- (Christianity) The religious service appointed to this hour.
- (historical) The first hour of daylight; the first canonical hour.
- The symbol ′ used to indicate feet, minutes, derivation and other measures and mathematical operations.
- (algebra, number theory) A prime element of a mathematical structure, particularly a prime number.
- The most active, thriving, or successful stage or period.
- A feather, from the wing of the cock ostrich, that is of the palest possible shade.
- (psychology) A stimulus which causes priming.
- The chief or best individual or part.
- An inch, as composed of twelve seconds in the duodecimal system.
- (backgammon) A series of consecutive blocks. A prime of six prevents the opponent's pieces from passing.
- (fencing) The first defensive position, with the sword hand held at head height, and the tip of the sword at head height.
- (card games) A four-card hand containing one card of each suit in the game of primero; the opposite of a flush in poker.
- Something which is first in importance or rank: a prime defense company, mortgage lender, etc.
- (film) Contraction of prime lens, a film lens.
- (cycling) An intermediate sprint within a race, usually offering a prize and/or points.
- (music) The first note or tone of a musical scale.
- the period of greatest prosperity or productivity
- a natural number that has exactly two distinct natural number divisors: 1 and itself
- the second canonical hour; about 6 a.m.
- the time of maturity when power and vigor are greatest
verb
- (mathematics) To mark with a prime mark.
- (transitive) To fill or prepare the chamber of a mechanism for its main work.
- To apply priming to (a musket or cannon); to apply a primer to (a metallic cartridge).
- (intransitive, of a steam boiler) To work so that foaming occurs from too violent ebullition, which causes water to become mixed with, and be carried along with, the steam that is formed.
- (intransitive) To serve as priming for the charge of a gun.
- To prepare; to make ready.
- (transitive) To apply a coat of primer paint to.
- fill with priming liquid
- cover with a primer; apply a primer to
- insert a primer into (a gun, mine, or charge) preparatory to detonation or firing
adj
- (of a module) In which any ascending chain of submodules eventually becomes constant.
- (of a topological space) In which any ascending chain of open subsets eventually becomes constant.
- (algebraic geometry, of a scheme) admitting a finite covering by open affine subsets operatorname SpecA_i, where each A_i is a noetherian ring;
- (mathematics, of a binary relation on a set) Such that the converse relation is well-founded (on that set).
- (of a group) In which any ascending chain of subgroups eventually becomes constant.
- (of a ring) In which any ascending chain of ideals eventually becomes constant.
adj
- (commutative algebra, not comparable, of a local ring) Noetherian and such that the minimal number of generators of the maximal ideal is equal to the Krull dimension of the ring.
- Demonstrating a consistent set of rules; showing order, evenness of operation or occurrence.
- (botany, zoology) Having all the parts of the same kind alike in size and shape.
- (chiefly US) Having the expected characteristics or appearances; normal, ordinary, standard.
- (geometry, of a polygon) Both equilateral and equiangular; having all sides of the same length, and all (corresponding) angles of the same size
- (astronomy) Of a moon or other satellite: following a relatively close and prograde orbit with little inclination or eccentricity.
- (Christianity) Bound by religious rule; belonging to a monastic or religious order (often as opposed to secular).
- (mathematical analysis, not comparable, of a Borel measure) Such that every set in its domain is both outer regular and inner regular.
- (colloquial) Exemplary; excellent example of; utter, downright.
- Happening at constant (especially short) intervals.
- (chiefly military) Permanently organised; being part of a set professional body of troops.
- Having bowel movements or menstrual periods at constant intervals in the expected way.
- (snowboarding) Riding with the left foot forward.
- (geometry, of a polyhedron) Whose faces are all congruent regular polygons, equally inclined to each other.
- (crystallography) Isometric.
- (algebraic geometry, not comparable, of a scheme) Such that the local ring at every point is regular.
- (grammar, of a verb, plural, etc) Following a set or common pattern; according to the general rules of a given language.
- Having a constant pattern; showing evenness of form or appearance.
- officially full-time
- in accordance with fixed order or procedure or principle
- regularly scheduled for fixed times
- symmetrically arranged
- conforming to a standard or pattern
- (used of the military) belonging to or engaged in by legitimate army forces
- not constipated
- in accord with regular practice or procedure
- relating to a person who does something regularly
- not deviating from what is normal
- often used as intensifiers
- occurring at fixed intervals
- (of solids) having clear dimensions that can be measured; volume can be determined with a suitable geometric formula
noun
- (Singapore) Synonym of regular serviceman; a member of the Singapore Armed Forces, Police Force or Civil Defence Force who has signed on, i.e., chosen to work full-time beyond their required length of national service.
- Anything that is normal or standard.
- A frequent customer, client or business partner.
- (Canada) A coffee with one cream and one sugar.
- A member of the armed forces or police force.
- A fixed number for each month serving to ascertain the day of the week, or the age of the moon, on the first day of any month.
- A member of the British Army (as opposed to a member of the Territorial Army or Reserve).
- A frequent, routine visitor to an establishment.
- A member of a religious order who has taken the three ordinary vows.
- A number for each year, giving, added to the concurrents, the number of the day of the week on which the Paschal full moon falls.
- (television) A character who appears in every episode of a TV series; a member of the regular cast.
- a soldier in the regular army
- a dependable follower (especially in party politics)
- a regular patron
- a garment size for persons of average height and weight
adj
noun
verb
adj
- (ring theory, of a local ring) Complete as a topological group with respect to its m-adic topology, where m is its unique maximal idea.
- (algebra, of a lattice) In which every set with a lower bound has a greatest lower bound.
- (computing theory, of a problem) That is in a given complexity class and is such that every other problem in the class can be reduced to it (usually in polynomial time or logarithmic space).
- With all parts included; with nothing missing; full.
- (logic, of a proof system of a formal system with respect to a given semantics) In which every semantically valid well-formed formula is provable.
- Generic intensifier.
- Finished; ended; concluded; completed.
- (mathematics, of a category) In which all small limits exist.
- (mathematical analysis, of a metric space or topological group) In which every Cauchy sequence converges to a point within the space.
- having every necessary or normal part or component or step
- highly skilled
- without qualification; used informally as (often pejorative) intensifiers
- having come or been brought to a conclusion
- perfect and complete in every respect; having all necessary qualities
noun
verb
- (transitive) To make whole or entire.
- (poker) To call from the small blind in an unraised pot.
- (ambitransitive) To finish; to make done; to reach the end.
- come or bring to a finish or an end
- write all the required information onto a form
- complete or carry out
- bring to a whole, with all the necessary parts or elements
- complete a pass
adj
- (commutative algebra, of a filtration (M_n) of a module M over a ring with respect to an ideal (here I but often a,m,p etc.) of that ring) Eventually satisfying the identity IM_n=M_n+1.
- (computer science, of a sorting algorithm) That maintains the relative order of items that compare as equal.
- (computing) Of software: established to be relatively free of bugs, as opposed to a beta version.
- Relatively unchanging, steady, permanent; firmly fixed or established; consistent; not easily moved, altered, or destroyed.
- firm and dependable; subject to little fluctuation
- showing little if any change
- resistant to change of position or condition
- not taking part readily in chemical change
- maintaining equilibrium
noun
- (professional wrestling) A group of wrestlers who support each other within a wrestling storyline.
- A building, wing or dependency set apart and adapted for lodging and feeding (and training) ungulates, especially horses.
- (slang) A group of prostitutes managed by one pimp.
- A group of people who are looked after, mentored, or trained in one place or for a particular purpose or profession.
- A coherent or consistent set of things (typically abstract) available or presented; array.
- (sumo) An organization of sumo wrestlers who live and train together.
- (Scotland) A set of advocates; a barristers' chambers.
- (metonymic) All the racehorses of a particular stable, i.e. belonging to a given owner.
- a farm building for housing horses or other livestock