n
(mathematics) Any member of a certain polynomial sequence whose nth term is of the form p_n(x)=x(x-an)ⁿ⁻¹.
adj
(group theory, of a group, semigroup, etc.) Whose operator is identified as addition.
n
(algebra) Any of certain algebraic objects (ring, field or vector space, etc., whose definition includes a commutative operation called addition) regarded as a group under addition.
n
(complex analysis, differential geometry) A geometric counterpart to Nevanlinna theory that extends the applicability of the concept of covering surface (of a topological space) by defining a covering number (a generalised "degree of covering") applicable to any bordered Riemann surface equipped with a conformal Riemannian metric.
n
(mathematics) A version of the Alexander polynomial that can be computed using a skein relation.
n
(algebra) A vector space (over some field) with an additional binary operation, a vector-valued product between vectors, which is bilinear over vector addition and scalar multiplication. (N.B.: such bilinearity implies distributivity of the vector multiplication with respect to the vector addition, which means that such a vector space is also a ring.)
n
(algebra, field theory, of a field F) A field G such that every polynomial over F splits completely over G (i.e., every element of G is a root of some polynomial over F and every root of every polynomial over F is an element of G).
n
(algebra, number theory) A real or complex number (more generally, an element of a number field) which is a root of a monic polynomial whose coefficients are integers; equivalently, an algebraic number whose minimal polynomial (lowest-degree polynomial of which it is a root and whose leading coefficient is 1) has integer coefficients.
n
(algebra, number theory) A complex number (more generally, an element of a number field) that is a root of a polynomial whose coefficients are integers; equivalently, a complex number (or element of a number field) that is a root of a monic polynomial whose coefficients are rational numbers.
adj
(algebra, field theory, of a field) Which contains as an element every root of every nonconstant univariate polynomial definable over it (i.e., over said field).
n
(mathematics) Any polynomial sequence p_n(x)_(n=0,1,2,…) satisfying the identity d/(dx)p_n(x)=np_n-1(x), and in which p_0(x) is a non-zero constant.
n
(algebra) A module over a ring together with an associative bilinear module-element-valued operator between module elements which together with the abelian group feature of the module makes a ring.
n
(mathematics) A result about injectivity and surjectivity of polynomials, often given as this special case: If P is an injective polynomial function from an n-dimensional complex vector space to itself then P is bijective. The full theorem generalizes to any algebraic variety over an algebraically closed field.
n
(mathematics) The limit of two (or more) objects, considered without regard to any arrows between them.
n
(group theory, ring theory) The subgroup (respectively, subring), denoted Z(G), of those elements of a given group (respectively, ring) G that commute with every element of G.
n
(linear algebra) The polynomial produced from a given square matrix by first subtracting the appropriate identity matrix multiplied by an indeterminant and then calculating the determinant.
n
(mathematics) The branch of algebra concerned with commutative rings and objects related to them (such as ideals and modules).
n
(algebra, ring theory) A ring whose multiplicative operation is commutative.
adj
(mathematics, of a category) In which all small limits exist.
n
(algebra, field theory, of an element of an extension field) Given a field extension L / K and an element α ∈ L, any other element β ∈ L that is another root of the minimal polynomial of α over K.
n
(algebra, group theory) The set that results from applying a group's binary operation with a given fixed element of the group on each element of a given subgroup.
n
(mathematics) A prime number that is a solution to one of two specific equations involving third powers of x and y. The two equations are p=(x³-y³)/(x-y),x=y+1,y>0 and p=(x³-y³)/(x-y),x=y+2,y>0.
n
The complement of an intersection is the union of the complements; as expressed by: (𝐴 ∩ 𝐵)′ = 𝐴′ ∪ 𝐵′
n
(linear algebra) A scalar that encodes certain characteristics of a given transformation matrix; the unique scalar function over square matrices which is distributive over matrix multiplication, multilinear in the rows and columns, and takes the value 1 for the unit matrix; abbreviated as: det.
n
(mathematics) The object obtained as the limit of a convergent sequence of directed graphs.
n
(mathematics) A theory of integral equations, concerning itself in the narrowest sense with the solution of the Fredholm integral equation.
n
(algebra) a free module over the ring of integers
n
(group theory) A group that has a presentation without relators; equivalently, a free product of some number of copies of ℤ.
n
(algebra) A module that has a basis. Equivalently, a module consisting of n-tuples of ring elements with no extra identities. (Then the number n is said to be its rank.) Equivalently, a direct sum whose summands are all the same ring. (The quantity of summands may be more than two.)
n
(algebra) A monoid whose underlying set is the Kleene closure of some set of generators, and whose operator is concatenation.
n
(mathematics) A group formed from others by concatenating their presentations (when those presentations are written with disjoint sets of generators).
n
(linear algebra) A method of reducing an augmented matrix to reduced row echelon form.
n
(mathematics) A first-order iterative optimization algorithm for finding a local minimum of a differentiable function.
n
(algebraic geometry) An important generalization of the Hirzebruch-Riemann-Roch theorem about complex manifolds.
n
(geometry, archaic) An effective divisor on a curve.
n
(algebra) Any one of the unital composition algebras identified by Hurwitz's theorem (on composition algebras) as solutions to the Hurwitz problem.
n
(mathematics) Synonym of Sendov's conjecture
n
(linear algebra) A generalization of the dot product for vectors of any dimensionality that may or may not be complex-numbered.
n
(algebra) A subset of the Cartesian product of all the members of an inverse system, such that a member M of the subset is a sort of “cross section” of the inverse system (as fiber bundle) induced by the morphisms of it. (If i
adj
Used to specify certain mathematical objects named in honour of C. G. J. Jacobi.
n
(mathematics, representation theory) A member P_(y,w)(q) of a certain family of integral polynomials that are indexed by pairs of elements y, w of a Coxeter group W, which can in particular be the Weyl group of a Lie group.
n
(mathematics) An expression for the determinant |B| of an n × n matrix B that is a weighted sum of the determinants of n submatrices (or minors) of B, each of size (n − 1) × (n − 1).
n
(mathematics) A module over a commutative ring with a bilinear product satisfying the Leibniz identity.
n
(algebra, field theory) For a given Galois field 𝔽_(qᵐ) and a suitable element β, a basis that has the form {β, β^q, β^(q2), ... , β^(qm-1)}.
n
(algebra) A bounded distributive lattice with a dual endomorphism (where “dual” means that it satisfies De Morgan’s laws).
n
(group theory, of an element of a group) For given group G and element g ∈ G, the smallest positive natural number n, if it exists, such that (using multiplicative notation), gⁿ = e, where e is the identity element of G; if no such number exists, the element is said to be of infinite order (or sometimes zero order).
n
(mathematics) A one-to-one mapping from a finite set to itself.
n
(mathematics) The dimension of a canonical ring.
adj
(mathematics) Locally the real part of a holomorphic function of several complex variables.
n
(mathematics) A subfunctor of the identity functor in the category of left modules over a ring with identity.
n
(algebra) A module which is a direct summand of a free module.
n
(mathematics) A specific type of operad
n
(linear algebra) The maximal number of linearly independent columns (or rows) of a matrix.
n
(mathematics) A geometric representation of the real number system.
n
(mathematics, linear algebra) Initialism of row echelon form. [(linear algebra) The stepped appearance of a matrix that has undergone Gaussian elimination with the result that the leading coefficient or pivot (that is, the first nonzero number from the left) of a nonzero row is to the right of the pivot of the row above it.]
n
(linear algebra) A relation between two matrices of the same size, such that every row of one matrix is a linear combination of the rows of the other matrix, and vice versa. It is an equivalence relation.
n
(mathematics) A certain approximation theorem in complex analysis.
adj
(linear algebra, of transformation) Having the property that the matrix of coefficients of the new variables has a determinant equal to zero.
n
(linear algebra, group theory) For given n, the group of n×n unitary matrices with complex elements and determinant equal to one.
n
(mathematics) a theorem providing conditions under which an operator or matrix can be diagonalized
n
(abstract algebra, algebraic geometry) The set, denoted Spec(R), of all prime ideals of a given ring R, commonly augmented with a Zariski topology and considered as a topological space.
adj
(algebra, of a short exact sequence) Having the middle group equal to the direct product of the others.
n
(mathematics) A group such that every injective cellular automaton with the group elements as its cells is also surjective.
n
(rare) Synonym of Lindemann-Weierstrass theorem
n
(mathematics) A determinant that is related to the linear independence of a set of solutions of a linear differential equation.
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