English-Wörter für 'A universal algebra.'
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noun
- A universal algebra.
- (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.
- 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.
- (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.
- the mathematics of generalized arithmetical operations
noun
- In universal algebra: an equational class; the class of all algebraic structures of a given signature, satisfying a given set of identities.
- A specific variation of something.
- (cybernetics) The total number of distinct states of a system; also, the logarithm to the base 2 of the total number of distinct states of a system.
- A deviation or difference.
- (radio, television, theater) Ellipsis of variety performance or variety show (“a type of entertainment featuring a succession of short, unrelated performances by various artistes such as (depending on the medium) acrobats, comedians, dancers, magicians, singers, etc.”).
- (linguistics) A specific form of a language, neutral to whether that form is an accent, dialect, register, etc., and to its prestige level; an isolect or lect.
- (radio, television, theater) The kind of entertainment given in variety performances or shows; also, the production of, or performance in, variety performances or shows.
- (algebraic geometry) Ellipsis of algebraic variety (“the set of solutions of a given system of polynomial equations over the real or complex numbers; any of certain generalisations of such a set that preserves the geometric intuition implicit in the original definition”).
- (botany, taxonomy) A rank in a taxonomic classification below species and (if present) subspecies, and above form; hence, an organism of that rank.
- A collection or number of different things.
- The quality of being varied; diversity.
- (philately) A stamp, or set of stamps, which has one or more characteristics (such as colour, paper, etc.) differing from other stamps in the same issue, especially if such differences are intentionally introduced.
- (biology, loosely) An animal or plant (or a group of such animals or plants) with characteristics causing it to differ from other animals or plants of the same species; a strain or cultivar.
- (biology) a taxonomic category consisting of members of a species that differ from others of the same species in minor but heritable characteristics
- a category of things distinguished by some common characteristic or quality
- noticeable heterogeneity
- a difference that is usually pleasant
- a collection containing a variety of sorts of things
- a show consisting of a series of short unrelated performances
adj
- (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.
- (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)
- 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
- (universal algebra) Any equivalence relation defined on an algebraic structure which is preserved by operations defined by the structure.
- (mathematics, linear algebra) Matrix similarity by an orthogonal matrix.
- (mathematics, geometry) The quality of being isometric — roughly, the same measure and shape.
- (psychology) A well-adjusted state or condition in which people are not lying to themselves or in denial.
- (mathematics, number theory) A relation between two numbers indicating they give the same remainder when divided by some given number.
- The quality of agreeing or corresponding; being suitable and appropriate.
- the quality of agreeing; being suitable and appropriate
adj
- Of, or relating to, algebra.
- of or relating to algebra
- (algebra, of a field) Whose every element is a root of some polynomial whose coefficients are rational.
- (chess, of notation) Describing squares by file (referred to in intrinsic order rather than by the piece starting on that file) and rank, both with reference to a fixed point rather than a player-dependent perspective.
- (algebra, number theory, of a number) Which is a root of some polynomial whose coefficients are rational.
- (mathematics, of an expression, equation, or function) Containing only numbers, letters, and arithmetic operators.
noun
- (algebra, universal algebra) Any one of the numerous types of mathematical object studied in algebra and especially in universal algebra.
- (more formally) A mathematical object comprising a carrier set (aka underlying set or domain), an optional scalar set, a set of operations (typically binary operations, but otherwise each of finite arity) and a set of identities (axioms) which the operations must satisfy.
noun
adj
name
adj
- (algebra, of a polynomial) Such that all its nonzero terms have the same degree.
- (linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero.
- (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.
- 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.
- (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
adj
- (algebra, of an ideal) Having its complement closed under multiplication.
- Early; blooming; being in the first stage.
- First in excellence, quality, or value.
- First in importance, degree, or rank.
- (algebra, of a nonzero module) Such that the annihilator of any nonzero submodule is equal to the annihilator of the whole module.
- First in time, order, or sequence.
- 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
adj
- (of an algebra over a commutative ring) Such that there exists some natural number n (called the index of the algebra) such that all products (of elements in the given algebra) of length n are zero.
- (Lie theory, of an element x of a Lie algebra L) Belonging to the derived algebra of L and such that the adjoint action of x is nilpotent (as a linear transformation on L).
- (Lie theory, of a Lie algebra) Such that the lower central series terminates.
- (ring theory, of an ideal I) Such that there exists a natural number k with Iᵏ = 0.
- (semigroup theory, of a semigroup with zero) Containing only nilpotent elements.
- (mathematics, algebra, ring theory, of an element x of a ring) Such that, for some positive integer n, xⁿ = 0.
- (group theory, of a group) Admitting a central series of finite length.
- equal to zero when raised to a certain power
adj
- (commutative algebra, of an ideal) Generated by differences of monomials.
- (algebraic geometry, of a stack) Any of several generalizations of the notion of toric varieties to stacks: the stack quotient of a toric variety by its torus; the stack quotient of a toric variety by a subgroup of its torus.
- (algebraic geometry, of a variety) Containing an algebraic torus as a dense subset, such that the group action of the torus on itself extends to the whole space; or, the embedding map taking the torus into the space. See Toric variety on Wikipedia.Wikipedia
- (geometry, algebra) Which, in any of several technical senses, admits a high degree of symmetry, allowing combinatorial methods to be used in its study.
- (error correction) A particular topological quantum error correcting code; see Toric code on Wikipedia.Wikipedia
- (geometry, of a manifold, generalizing the case of toric varieties) (Narrowly) A compact smooth toric variety. (Broadly) Quasitoric: a closed, real, even-dimensional smooth manifold equipped with an effective, smooth action by an algebraic torus whose orbits are simple complex polytopes and such that the action is locally the same as a faithful real representation of the group.
noun
adj
- (linear algebra, of a function in two variables) Linear (preserving linear combinations) in each variable.
- (complex analysis, physics, engineering) Of or pertaining to a Möbius transformation (type of conformal map representable as the ratio of two linear functions).
- linear with respect to each of two variables or positions
adj
- (algebra, of an algebraic structure) Having a commutative operation.
- (mathematics, of a binary operation) Such that the order in which the operands are taken does not affect their image under the operation.
- Relating to exchange; interchangeable.
- (mathematics, of a diagram of morphisms) Such that any two sequences of morphisms with the same initial and final positions compose to the same morphism.
- (of a binary operation) independent of order; as in e.g.: ‘a x b’ = ‘b x a’
noun
- (commutative algebra) Clipping of uniformizing parameter.
- (programming, loosely) An actual value given to such a formal parameter.
- A value kept constant during an experiment, equation, calculation, or similar, but varied over other versions of the experiment, equation, calculation, etc.
- (crystallography) The ratio of the three crystallographic axes which determines the position of any plane.
- (sciences) A variable that describes a property or characteristic of some system (material, object, event, etc.) or some aspect thereof.
- (geometry) In the ellipse and hyperbola, a third proportional to any diameter and its conjugate, or in the parabola, to any abscissa and the corresponding ordinate.
- (programming) An input variable of a function definition, that gets an actual value (argument) at execution time.
- A characteristic or feature that distinguishes something from others.
- (crystallography) The fundamental axial ratio for a given species.
- (statistics) Any measured quantity of a statistical population that summarises or describes an aspect of the population.
- (machine learning) A variable of a model that is trained by a machine learning algorithm.
- a constant in the equation of a curve that can be varied to yield a family of similar curves
- any factor that defines a system and determines (or limits) its performance
- a quantity (such as the mean or variance) that characterizes a statistical population and that can be estimated by calculations from sample data
- (computer science) a reference or value that is passed to a function, procedure, subroutine, command, or program
noun
- (algebra, ring theory) Initialism of central simple algebra.
- (algebra, Lie theory) Initialism of Cartan subalgebra.
- (countable) Initialism of community service announcement.
- (uncountable) Initialism of child sexual abuse.
- (US) Initialism of combined statistical area.
- (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.
name
noun
noun
- (commutative algebra, of an ideal) Height.
- (astronomy) The angular distance of a heavenly body above our Earth's horizon.
- (geometry) The line perpendicularly connecting a figure’s vertex, especially a triangle’s apex, to the side opposite to the vertex.
- Highest point or degree.
- The absolute height of a location, usually measured from sea level.
- (geometry) The length of such a line; the distance measured perpendicularly from a figure's vertex to the side opposite to the vertex.
- Height of rank or excellence; superiority.
- A vertical distance.
- elevation especially above sea level or above the earth's surface
- angular distance above the horizon (especially of a celestial object)
- the perpendicular distance from the base of a geometric figure to the opposite vertex (or side if parallel)
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)
noun
- A universal algebra.
- (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.
- 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.
- (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.
- the mathematics of generalized arithmetical operations
noun
- In universal algebra: an equational class; the class of all algebraic structures of a given signature, satisfying a given set of identities.
- A specific variation of something.
- (cybernetics) The total number of distinct states of a system; also, the logarithm to the base 2 of the total number of distinct states of a system.
- A deviation or difference.
- (radio, television, theater) Ellipsis of variety performance or variety show (“a type of entertainment featuring a succession of short, unrelated performances by various artistes such as (depending on the medium) acrobats, comedians, dancers, magicians, singers, etc.”).
- (linguistics) A specific form of a language, neutral to whether that form is an accent, dialect, register, etc., and to its prestige level; an isolect or lect.
- (radio, television, theater) The kind of entertainment given in variety performances or shows; also, the production of, or performance in, variety performances or shows.
- (algebraic geometry) Ellipsis of algebraic variety (“the set of solutions of a given system of polynomial equations over the real or complex numbers; any of certain generalisations of such a set that preserves the geometric intuition implicit in the original definition”).
- (botany, taxonomy) A rank in a taxonomic classification below species and (if present) subspecies, and above form; hence, an organism of that rank.
- A collection or number of different things.
- The quality of being varied; diversity.
- (philately) A stamp, or set of stamps, which has one or more characteristics (such as colour, paper, etc.) differing from other stamps in the same issue, especially if such differences are intentionally introduced.
- (biology, loosely) An animal or plant (or a group of such animals or plants) with characteristics causing it to differ from other animals or plants of the same species; a strain or cultivar.
- (biology) a taxonomic category consisting of members of a species that differ from others of the same species in minor but heritable characteristics
- a category of things distinguished by some common characteristic or quality
- noticeable heterogeneity
- a difference that is usually pleasant
- a collection containing a variety of sorts of things
- a show consisting of a series of short unrelated performances
noun
- (universal algebra) Any equivalence relation defined on an algebraic structure which is preserved by operations defined by the structure.
- (mathematics, linear algebra) Matrix similarity by an orthogonal matrix.
- (mathematics, geometry) The quality of being isometric — roughly, the same measure and shape.
- (psychology) A well-adjusted state or condition in which people are not lying to themselves or in denial.
- (mathematics, number theory) A relation between two numbers indicating they give the same remainder when divided by some given number.
- The quality of agreeing or corresponding; being suitable and appropriate.
- the quality of agreeing; being suitable and appropriate
noun
- (algebra, universal algebra) Any one of the numerous types of mathematical object studied in algebra and especially in universal algebra.
- (more formally) A mathematical object comprising a carrier set (aka underlying set or domain), an optional scalar set, a set of operations (typically binary operations, but otherwise each of finite arity) and a set of identities (axioms) which the operations must satisfy.
noun
adj
name
noun
adj
- (of an algebra over a commutative ring) Such that there exists some natural number n (called the index of the algebra) such that all products (of elements in the given algebra) of length n are zero.
- (Lie theory, of an element x of a Lie algebra L) Belonging to the derived algebra of L and such that the adjoint action of x is nilpotent (as a linear transformation on L).
- (Lie theory, of a Lie algebra) Such that the lower central series terminates.
- (ring theory, of an ideal I) Such that there exists a natural number k with Iᵏ = 0.
- (semigroup theory, of a semigroup with zero) Containing only nilpotent elements.
- (mathematics, algebra, ring theory, of an element x of a ring) Such that, for some positive integer n, xⁿ = 0.
- (group theory, of a group) Admitting a central series of finite length.
- equal to zero when raised to a certain power
noun
adj
- (linear algebra, of a function in two variables) Linear (preserving linear combinations) in each variable.
- (complex analysis, physics, engineering) Of or pertaining to a Möbius transformation (type of conformal map representable as the ratio of two linear functions).
- linear with respect to each of two variables or positions
noun
- (commutative algebra) Clipping of uniformizing parameter.
- (programming, loosely) An actual value given to such a formal parameter.
- A value kept constant during an experiment, equation, calculation, or similar, but varied over other versions of the experiment, equation, calculation, etc.
- (crystallography) The ratio of the three crystallographic axes which determines the position of any plane.
- (sciences) A variable that describes a property or characteristic of some system (material, object, event, etc.) or some aspect thereof.
- (geometry) In the ellipse and hyperbola, a third proportional to any diameter and its conjugate, or in the parabola, to any abscissa and the corresponding ordinate.
- (programming) An input variable of a function definition, that gets an actual value (argument) at execution time.
- A characteristic or feature that distinguishes something from others.
- (crystallography) The fundamental axial ratio for a given species.
- (statistics) Any measured quantity of a statistical population that summarises or describes an aspect of the population.
- (machine learning) A variable of a model that is trained by a machine learning algorithm.
- a constant in the equation of a curve that can be varied to yield a family of similar curves
- any factor that defines a system and determines (or limits) its performance
- a quantity (such as the mean or variance) that characterizes a statistical population and that can be estimated by calculations from sample data
- (computer science) a reference or value that is passed to a function, procedure, subroutine, command, or program
noun
- (algebra, ring theory) Initialism of central simple algebra.
- (algebra, Lie theory) Initialism of Cartan subalgebra.
- (countable) Initialism of community service announcement.
- (uncountable) Initialism of child sexual abuse.
- (US) Initialism of combined statistical area.
- (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
- (commutative algebra, of an ideal) Height.
- (astronomy) The angular distance of a heavenly body above our Earth's horizon.
- (geometry) The line perpendicularly connecting a figure’s vertex, especially a triangle’s apex, to the side opposite to the vertex.
- Highest point or degree.
- The absolute height of a location, usually measured from sea level.
- (geometry) The length of such a line; the distance measured perpendicularly from a figure's vertex to the side opposite to the vertex.
- Height of rank or excellence; superiority.
- A vertical distance.
- elevation especially above sea level or above the earth's surface
- angular distance above the horizon (especially of a celestial object)
- the perpendicular distance from the base of a geometric figure to the opposite vertex (or side if parallel)
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adj
- (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.
- (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)
- 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
- Of, or relating to, algebra.
- of or relating to algebra
- (algebra, of a field) Whose every element is a root of some polynomial whose coefficients are rational.
- (chess, of notation) Describing squares by file (referred to in intrinsic order rather than by the piece starting on that file) and rank, both with reference to a fixed point rather than a player-dependent perspective.
- (algebra, number theory, of a number) Which is a root of some polynomial whose coefficients are rational.
- (mathematics, of an expression, equation, or function) Containing only numbers, letters, and arithmetic operators.
adj
- (algebra, of a polynomial) Such that all its nonzero terms have the same degree.
- (linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero.
- (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.
- 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.
- (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
adj
- (algebra, of an ideal) Having its complement closed under multiplication.
- Early; blooming; being in the first stage.
- First in excellence, quality, or value.
- First in importance, degree, or rank.
- (algebra, of a nonzero module) Such that the annihilator of any nonzero submodule is equal to the annihilator of the whole module.
- First in time, order, or sequence.
- 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
adj
- (of an algebra over a commutative ring) Such that there exists some natural number n (called the index of the algebra) such that all products (of elements in the given algebra) of length n are zero.
- (Lie theory, of an element x of a Lie algebra L) Belonging to the derived algebra of L and such that the adjoint action of x is nilpotent (as a linear transformation on L).
- (Lie theory, of a Lie algebra) Such that the lower central series terminates.
- (ring theory, of an ideal I) Such that there exists a natural number k with Iᵏ = 0.
- (semigroup theory, of a semigroup with zero) Containing only nilpotent elements.
- (mathematics, algebra, ring theory, of an element x of a ring) Such that, for some positive integer n, xⁿ = 0.
- (group theory, of a group) Admitting a central series of finite length.
- equal to zero when raised to a certain power
adj
- (commutative algebra, of an ideal) Generated by differences of monomials.
- (algebraic geometry, of a stack) Any of several generalizations of the notion of toric varieties to stacks: the stack quotient of a toric variety by its torus; the stack quotient of a toric variety by a subgroup of its torus.
- (algebraic geometry, of a variety) Containing an algebraic torus as a dense subset, such that the group action of the torus on itself extends to the whole space; or, the embedding map taking the torus into the space. See Toric variety on Wikipedia.Wikipedia
- (geometry, algebra) Which, in any of several technical senses, admits a high degree of symmetry, allowing combinatorial methods to be used in its study.
- (error correction) A particular topological quantum error correcting code; see Toric code on Wikipedia.Wikipedia
- (geometry, of a manifold, generalizing the case of toric varieties) (Narrowly) A compact smooth toric variety. (Broadly) Quasitoric: a closed, real, even-dimensional smooth manifold equipped with an effective, smooth action by an algebraic torus whose orbits are simple complex polytopes and such that the action is locally the same as a faithful real representation of the group.
adj
- (algebra, of an algebraic structure) Having a commutative operation.
- (mathematics, of a binary operation) Such that the order in which the operands are taken does not affect their image under the operation.
- Relating to exchange; interchangeable.
- (mathematics, of a diagram of morphisms) Such that any two sequences of morphisms with the same initial and final positions compose to the same morphism.
- (of a binary operation) independent of order; as in e.g.: ‘a x b’ = ‘b x a’
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)