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adj
- (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.
- (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.
- 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
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.
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
- (algebra, ring theory) A basis of a polynomial ring (said ring being viewed either as a vector space over the field of coefficients or as a free module over the ring of coefficients).
- (algebra, field theory, cryptography, of a finite field) Specifically, a basis, of the form {1, α, ..., αⁿ⁻¹}, of a finite extension F_(qⁿ) of a Galois field F_q, where α is a primitive element of F_(qⁿ) (i.e., a root of a degree-n primitive polynomial over F_q).
adj
- (ring theory, by extension) (of two or more ideals of a ring) Whose sum is the whole ring; (of two or more elements of a ring) generating the whole ring.
- (number theory, of a positive integer) Having no positive integer factors, aside from 1, in common with one or more specified other positive integers.
- (number theory, of two or more positive integers) Having no positive integer factors in common, aside from 1.
- (algebra, by extension, of two or more polynomials) Whose greatest common divisor is a nonzero constant (i.e., polynomial of degree 0).
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
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
verb
- (transitive) To surround or fit with a ring, or as if with a ring.
- (transitive) To enclose or surround.
- (intransitive) to resound, reverberate, echo.
- (transitive) To attach a ring to, especially for identification.
- To ring up (enter into a cash register or till)
- (intransitive, figuratively) To produce the sound of a bell or a similar sound.
- (transitive, colloquial, British, Australia, New Zealand) To telephone (someone).
- (Australia, transitive) To ride around (a group of animals, especially cattle) to keep them milling in one place; hence (intransitive), to work as a drover, to muster cattle.
- (transitive, figuratively) To make an incision around; to girdle; to cut away a circular tract of bark from a tree in order to kill it.
- (transitive) To make (a bell, etc.) produce a resonant sound.
- (intransitive) Of a bell, etc., to produce a resonant sound.
- (transitive) To steal and change the identity of (cars) in order to resell them.
- (transitive) To produce (a sound) by ringing.
- (falconry) To rise in the air spirally.
- (intransitive) To produce music with bells.
- (intransitive, figuratively) Of something spoken or written, to appear to be, to seem, to sound.
- sound loudly and sonorously
- ring or echo with sound
- attach a ring to the foot of, in order to identify
- get or try to get into communication (with someone) by telephone
- make (bells) ring, often for the purposes of musical edification
- extend on all sides of simultaneously; encircle
noun
- (colloquial) A telephone call.
- (typography) A diacritical mark in the shape of a hollow circle placed above or under the letter; a kroužek.
- Any loud sound; the sound of numerous voices; a sound continued, repeated, or reverberated.
- In a jack plug, the connector between the tip and the sleeve.
- (Internet) Ellipsis of webring.
- A circular group of people or objects.
- (astronomy) A formation of various pieces of material orbiting around a planet or young star.
- (vulgar) The rectum, anus, or anal sphincters.
- (historical) An instrument, formerly used for taking the sun's altitude, consisting of a brass ring suspended by a swivel, with a hole at one side through which a solar ray entering indicated the altitude on the graduated inner surface opposite.
- (chemistry) A group of atoms linked by bonds to form a closed chain in a molecule.
- A piece of food in the shape of a ring.
- An exclusive group of people, usually involving some unethical or illegal practices.
- (mathematical analysis, measure theory) A family of sets that is closed under finite unions and set-theoretic differences.
- (geometry) A planar geometrical figure included between two concentric circles.
- (historical) An old English measure of corn equal to the coomb or half a quarter.
- The resonant sound of a bell, or a sound resembling it.
- A chime, or set of bells harmonically tuned.
- (algebra) An algebraic structure as above, but only required to be a semigroup under the multiplicative operation, that is, there need not be a multiplicative identity element.
- (figuratively) A sound or appearance that is characteristic of something.
- A long stripe of contrastive material, colour, etc, that encircles something.
- (computing theory) A hierarchical level of privilege in a computer system, usually at hardware level, used to protect data and functionality (also protection ring).
- (British) A large circular prehistoric stone construction such as Stonehenge.
- A circumscribing object, (roughly) circular and hollow, looking like an annual ring, earring, finger ring etc.
- A place where some sports or exhibitions take place; notably a circular or comparable arena, such as a boxing ring or a circus ring; hence the field of a political contest.
- (jewelry) A round piece of (precious) metal worn around the finger or through the ear, nose, etc.
- (algebra) An algebraic structure which consists of a set with two binary operations: an additive operation and a multiplicative operation, such that the set is an abelian group under the additive operation, a monoid under the multiplicative operation, and such that the multiplicative operation is distributive with respect to the additive operation.
- (networking) A network topology where connected devices form a circular data channel. All computers on the ring can see every message, and there are no collisions, and a single point of failure will occur if any part of the ring breaks.
- (firearms) Either of the pair of clamps used to hold a telescopic sight to a rifle.
- (figuratively) A pleasant or correct sound.
- (UK) A burner on a kitchen stove.
- The open space in front of a racecourse stand, used for betting purposes.
- (cartomancy) The twenty-fifth Lenormand card.
- (botany) A flexible band partly or wholly encircling the spore cases of ferns.
- (UK) A bird band, a round piece of metal put around a bird's leg used for identification and studies of migration.
- (mathematics, order theory) A family of sets closed under finite union and finite intersection.
- a strip of material attached to the leg of a bird to identify it (as in studies of bird migration)
- a platform usually marked off by ropes in which contestants box or wrestle
- (chemistry) a chain of atoms in a molecule that forms a closed loop
- an association of criminals
- a rigid circular band of metal or wood or other material used for holding or fastening or hanging or pulling
- a characteristic sound
- jewelry consisting of a circlet of precious metal (often set with jewels) worn on the finger
- the sound of a bell ringing
- a toroidal shape
noun
- (UK dialectal) A ring; a circle.
- (UK dialectal) A man, especially a warrior or hero.
- A sheet of ice prepared for playing certain sports, such as hockey or curling.
- A building housing an ice rink.
- A surface for roller skating.
- (curling) A team in a competition.
- building that contains a surface for ice skating or roller skating
verb
noun
- A lock, tress.
- (entomology) Any of various butterflies with small rings on the wings, in the tribe Satyrini of the family Nymphalidae, such as Aphantopus hyperantus.
- A small ring.
- any of various butterflies belonging to the family Satyridae
- a round shape formed by a series of concentric circles (as formed by leaves or flower petals)
- a little ring
- lock of hair in the shape of a spiral or curl
noun
noun
adj
- (ring theory, of an element of a graded ring) Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)
- (of a linear differential equation) Having its degree-zero term equal to zero; admitting the trivial solution.
- (algebra, of a polynomial) Such that all its nonzero terms have the same degree.
- Having the same composition throughout; of uniform make-up.
- (probability theory, Fourier analysis, of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)) Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m.
- Of the same kind; alike, similar.
- (of a linear map f between vector spaces graded by a commutative monoid I) Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I.
- (geometry, of a space equipped with a group action) Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful).
- (set theory, order theory, of a relation) Holding between a set and itself; being an endorelation.
- (of a first-order differential equation) Capable of being written in the form f(x,y) mathop dy=g(x,y) mathop dx where f and g are homogeneous functions of the same degree as each other.
- (linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero.
- (mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).
- (geometry) Of or relating to homogeneous coordinates.
- The function f(x,y)#61;x²#43;x²ʸ#43;y² is not homogeneous on all of #92;mathbb#123;R#125;² because f(2,2)#61;16#92;neq 2ᵏ#42;3#61;2ᵏf(1,1) for any k, but f is homogeneous on the subspace of #92;mathbb#123;R#125;² spanned by (1,0) because f(#92;alphax,#92;alphay)#61;#92;alphax²#61;#92;alpha²f(x,y) for all (x,y)#92;in#92;operatorname#123;Span#125;#92;#123;(1,0)#92;#125;.
- (mathematical analysis, generalizing the case of polynomial functions, of a function f) Such that if each of f 's inputs are multiplied by the same scalar, f 's output is multiplied by the same scalar to some fixed power (called the degree of homogeneity or degree of f). (Formally and more generally, of a partial function f between vector spaces whose domain is a linear cone) Satisfying the equality f(s mathbf x)=sᵏᶠ(
- (of a general differential equation) Homogeneous as a function of the dependent variable and its derivatives.
- (chemistry) In the same state of matter.
- all of the same or similar kind or nature
noun
- plural of ring
- (post-mid century) Ellipsis of still rings.
- A traditional Irish game of throwing rings onto hooks.
- (gymnastics) A gymnastics apparatus and discipline consisting of two rings suspended from a bar.
- gymnastic apparatus consisting of a pair of heavy metal circles (usually covered with leather) suspended by ropes; used for gymnastic exercises
verb
noun
- (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".
- (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.
- (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).
- (algebra, ring theory, of a module) The intersection of maximal submodules of a given module.
- (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
- (UK, slang) A large, garish ring; a sovereign ring.
- Ellipsis of sovereign citizen.
- A former Australian gold coin, minted from 1855–1931, of one pound value.
- A very large champagne bottle with the capacity of about 25 liters, equivalent to 33+¹⁄₃ standard bottles.
- A gold coin of the United Kingdom, with a nominal value of one pound sterling but in practice used as a bullion coin.
- One who is not a subject to a ruler or nation.
- Any butterfly of the tribe Nymphalini, or genus Basilarchia, eg., ursula, viceroy.
- A monarch; the ruler of a country.
- a nation's ruler or head of state usually by hereditary right
adj
verb
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
- (algebra, ring theory) A basis of a polynomial ring (said ring being viewed either as a vector space over the field of coefficients or as a free module over the ring of coefficients).
- (algebra, field theory, cryptography, of a finite field) Specifically, a basis, of the form {1, α, ..., αⁿ⁻¹}, of a finite extension F_(qⁿ) of a Galois field F_q, where α is a primitive element of F_(qⁿ) (i.e., a root of a degree-n primitive polynomial over F_q).
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
- (UK dialectal) A ring; a circle.
- (UK dialectal) A man, especially a warrior or hero.
- A sheet of ice prepared for playing certain sports, such as hockey or curling.
- A building housing an ice rink.
- A surface for roller skating.
- (curling) A team in a competition.
- building that contains a surface for ice skating or roller skating
noun
noun
noun
- plural of ring
- (post-mid century) Ellipsis of still rings.
- A traditional Irish game of throwing rings onto hooks.
- (gymnastics) A gymnastics apparatus and discipline consisting of two rings suspended from a bar.
- gymnastic apparatus consisting of a pair of heavy metal circles (usually covered with leather) suspended by ropes; used for gymnastic exercises
verb
noun
- (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".
- (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.
- (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).
- (algebra, ring theory, of a module) The intersection of maximal submodules of a given module.
- (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
- (UK, slang) A large, garish ring; a sovereign ring.
- Ellipsis of sovereign citizen.
- A former Australian gold coin, minted from 1855–1931, of one pound value.
- A very large champagne bottle with the capacity of about 25 liters, equivalent to 33+¹⁄₃ standard bottles.
- A gold coin of the United Kingdom, with a nominal value of one pound sterling but in practice used as a bullion coin.
- One who is not a subject to a ruler or nation.
- Any butterfly of the tribe Nymphalini, or genus Basilarchia, eg., ursula, viceroy.
- A monarch; the ruler of a country.
- a nation's ruler or head of state usually by hereditary right
adj
verb
verb
- (transitive) To surround or fit with a ring, or as if with a ring.
- (transitive) To enclose or surround.
- (intransitive) to resound, reverberate, echo.
- (transitive) To attach a ring to, especially for identification.
- To ring up (enter into a cash register or till)
- (intransitive, figuratively) To produce the sound of a bell or a similar sound.
- (transitive, colloquial, British, Australia, New Zealand) To telephone (someone).
- (Australia, transitive) To ride around (a group of animals, especially cattle) to keep them milling in one place; hence (intransitive), to work as a drover, to muster cattle.
- (transitive, figuratively) To make an incision around; to girdle; to cut away a circular tract of bark from a tree in order to kill it.
- (transitive) To make (a bell, etc.) produce a resonant sound.
- (intransitive) Of a bell, etc., to produce a resonant sound.
- (transitive) To steal and change the identity of (cars) in order to resell them.
- (transitive) To produce (a sound) by ringing.
- (falconry) To rise in the air spirally.
- (intransitive) To produce music with bells.
- (intransitive, figuratively) Of something spoken or written, to appear to be, to seem, to sound.
- sound loudly and sonorously
- ring or echo with sound
- attach a ring to the foot of, in order to identify
- get or try to get into communication (with someone) by telephone
- make (bells) ring, often for the purposes of musical edification
- extend on all sides of simultaneously; encircle
noun
- (colloquial) A telephone call.
- (typography) A diacritical mark in the shape of a hollow circle placed above or under the letter; a kroužek.
- Any loud sound; the sound of numerous voices; a sound continued, repeated, or reverberated.
- In a jack plug, the connector between the tip and the sleeve.
- (Internet) Ellipsis of webring.
- A circular group of people or objects.
- (astronomy) A formation of various pieces of material orbiting around a planet or young star.
- (vulgar) The rectum, anus, or anal sphincters.
- (historical) An instrument, formerly used for taking the sun's altitude, consisting of a brass ring suspended by a swivel, with a hole at one side through which a solar ray entering indicated the altitude on the graduated inner surface opposite.
- (chemistry) A group of atoms linked by bonds to form a closed chain in a molecule.
- A piece of food in the shape of a ring.
- An exclusive group of people, usually involving some unethical or illegal practices.
- (mathematical analysis, measure theory) A family of sets that is closed under finite unions and set-theoretic differences.
- (geometry) A planar geometrical figure included between two concentric circles.
- (historical) An old English measure of corn equal to the coomb or half a quarter.
- The resonant sound of a bell, or a sound resembling it.
- A chime, or set of bells harmonically tuned.
- (algebra) An algebraic structure as above, but only required to be a semigroup under the multiplicative operation, that is, there need not be a multiplicative identity element.
- (figuratively) A sound or appearance that is characteristic of something.
- A long stripe of contrastive material, colour, etc, that encircles something.
- (computing theory) A hierarchical level of privilege in a computer system, usually at hardware level, used to protect data and functionality (also protection ring).
- (British) A large circular prehistoric stone construction such as Stonehenge.
- A circumscribing object, (roughly) circular and hollow, looking like an annual ring, earring, finger ring etc.
- A place where some sports or exhibitions take place; notably a circular or comparable arena, such as a boxing ring or a circus ring; hence the field of a political contest.
- (jewelry) A round piece of (precious) metal worn around the finger or through the ear, nose, etc.
- (algebra) An algebraic structure which consists of a set with two binary operations: an additive operation and a multiplicative operation, such that the set is an abelian group under the additive operation, a monoid under the multiplicative operation, and such that the multiplicative operation is distributive with respect to the additive operation.
- (networking) A network topology where connected devices form a circular data channel. All computers on the ring can see every message, and there are no collisions, and a single point of failure will occur if any part of the ring breaks.
- (firearms) Either of the pair of clamps used to hold a telescopic sight to a rifle.
- (figuratively) A pleasant or correct sound.
- (UK) A burner on a kitchen stove.
- The open space in front of a racecourse stand, used for betting purposes.
- (cartomancy) The twenty-fifth Lenormand card.
- (botany) A flexible band partly or wholly encircling the spore cases of ferns.
- (UK) A bird band, a round piece of metal put around a bird's leg used for identification and studies of migration.
- (mathematics, order theory) A family of sets closed under finite union and finite intersection.
- a strip of material attached to the leg of a bird to identify it (as in studies of bird migration)
- a platform usually marked off by ropes in which contestants box or wrestle
- (chemistry) a chain of atoms in a molecule that forms a closed loop
- an association of criminals
- a rigid circular band of metal or wood or other material used for holding or fastening or hanging or pulling
- a characteristic sound
- jewelry consisting of a circlet of precious metal (often set with jewels) worn on the finger
- the sound of a bell ringing
- a toroidal shape
verb
noun
- A lock, tress.
- (entomology) Any of various butterflies with small rings on the wings, in the tribe Satyrini of the family Nymphalidae, such as Aphantopus hyperantus.
- A small ring.
- any of various butterflies belonging to the family Satyridae
- a round shape formed by a series of concentric circles (as formed by leaves or flower petals)
- a little ring
- lock of hair in the shape of a spiral or curl
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adj
- (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.
- (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.
- 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
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
- (ring theory, by extension) (of two or more ideals of a ring) Whose sum is the whole ring; (of two or more elements of a ring) generating the whole ring.
- (number theory, of a positive integer) Having no positive integer factors, aside from 1, in common with one or more specified other positive integers.
- (number theory, of two or more positive integers) Having no positive integer factors in common, aside from 1.
- (algebra, by extension, of two or more polynomials) Whose greatest common divisor is a nonzero constant (i.e., polynomial of degree 0).
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 element of a graded ring) Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)
- (of a linear differential equation) Having its degree-zero term equal to zero; admitting the trivial solution.
- (algebra, of a polynomial) Such that all its nonzero terms have the same degree.
- Having the same composition throughout; of uniform make-up.
- (probability theory, Fourier analysis, of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)) Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m.
- Of the same kind; alike, similar.
- (of a linear map f between vector spaces graded by a commutative monoid I) Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I.
- (geometry, of a space equipped with a group action) Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful).
- (set theory, order theory, of a relation) Holding between a set and itself; being an endorelation.
- (of a first-order differential equation) Capable of being written in the form f(x,y) mathop dy=g(x,y) mathop dx where f and g are homogeneous functions of the same degree as each other.
- (linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero.
- (mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).
- (geometry) Of or relating to homogeneous coordinates.
- The function f(x,y)#61;x²#43;x²ʸ#43;y² is not homogeneous on all of #92;mathbb#123;R#125;² because f(2,2)#61;16#92;neq 2ᵏ#42;3#61;2ᵏf(1,1) for any k, but f is homogeneous on the subspace of #92;mathbb#123;R#125;² spanned by (1,0) because f(#92;alphax,#92;alphay)#61;#92;alphax²#61;#92;alpha²f(x,y) for all (x,y)#92;in#92;operatorname#123;Span#125;#92;#123;(1,0)#92;#125;.
- (mathematical analysis, generalizing the case of polynomial functions, of a function f) Such that if each of f 's inputs are multiplied by the same scalar, f 's output is multiplied by the same scalar to some fixed power (called the degree of homogeneity or degree of f). (Formally and more generally, of a partial function f between vector spaces whose domain is a linear cone) Satisfying the equality f(s mathbf x)=sᵏᶠ(
- (of a general differential equation) Homogeneous as a function of the dependent variable and its derivatives.
- (chemistry) In the same state of matter.
- all of the same or similar kind or nature