n
(mathematics) Any algebra in which multiplication (or its equivalent) is commutative.
n
(harmonic analysis, representation theory, topology) A branch of harmonic analysis dealing with generalised Fourier transforms that act on functions defined on Hausdorff locally compact topological groups.
adj
(algebra, of a module) in which any descending chain of submodules eventually starts repeating.
n
(mathematics) A group constructed from two subgroups by generalization of the direct and semidirect products.
n
(mathematics) A representation of a Clifford algebra.
n
(mathematics, linear algebra, of a matrix) The signed determinant of the submatrix produced by removing the row and column containing a specified element; primarily used in the recursive definition and calculation of the determinant of a matrix.
n
(combinatorics) An element in a matroid that belongs to no circuit or (equivalently) belongs to every basis.
n
(mathematics) A theorem in operator theory, stating that, if T is a contraction on a Hilbert space H, and U is its minimal unitary dilation acting on some Hilbert space K, and R is an operator on H commuting with T, then there is an operator S on K commuting with U such that RTⁿ=P_HSUⁿ|_H;∀n≥0, and ‖S‖=‖R‖. In other words, an operator from the commutant of T can be "lifted" to an operator in the commutant of the unitary dilation of T.
n
(algebra) Any algebra (mathematical structure) in which the multiplication operation is commutative.
n
The supremum, over all elements of a given group's derived subgroup, of their commutator lengths.
n
(mathematics) The branch of mathematics that studies holomorphic functions.
n
A set of formal languages with certain desirable closure properties, in particular those of the regular languages, the context-free languages and the recursively enumerable languages.
n
(algebra) A subset of a group which is an equivalence class in the quotient set of the group divided by conjugation as equivalence relation.
n
(mathematics) A mapping sending x to gxg⁻¹, where g and x are elements of a group; inner automorphism
n
(mathematics) One of a set of composed operads
n
(mathematics) The colimit of two (or more) objects, without regard to any morphisms between them.
n
(mathematics, braid theory) A left-invariant total order on the braid group.
n
The subgroup of a specified group generated by the larger group's commutators.
n
(algebra) A lattice in which the "meet" and the "join" operations are distributive with respect to each other.
n
(mathematics) A method of computing the determinants of a square matrix by constructing a series of sequentially smaller matrices.
n
(mathematics) One of the entries of a matrix.
n
(algebra, Galois theory) A subfield of a given field which contains all of the fixed points that are common to all of the automorphisms of some subgroup of the automorphism group of that given field.
n
(mathematics) Used attributively to attribute a concept to the work of Ferdinand Georg Frobenius or more directly to associate it with the Frobenius endomorphism (commutative algebra, field theory) or Frobenius morphism (category theory).
n
(algebra, Galois theory) An algebraic extension that is both a normal and a separable extension; equivalently, an algebraic extension E/F such that the fixed field of its automorphism group (Galois group) Aut(E/F) is the base field F.
n
(linear algebra) A method of reducing an augmented matrix to row echelon form.
n
(mathematics) An equivalence class that includes a specified function defined in an open neighborhood.
n
the d-dimensional Hausdorff content of S is defined by C_Hᵈ(S):= lim _(sup ᵢr_i→0) inf Bigl ∑ᵢr_iᵈ:thereisacoverofSbyballswithradiir_i>0 Bigr.
n
(mathematical analysis) In the abstract metric space of all compact subsets of ℝⁿ, given a pair of compact sets A and B, the Hausdorff metric is h(A,B)= mbox max𝜌(A,B),𝜌(B,A) where 𝜌(A,B)= sup _(a∈A) inf _(b∈B),d(a,b), where d is the Euclidean metric in ℝⁿ.
n
(mathematics) The formal group ring of a formal group law.
n
(mathematics) An ideal of a semihypergroup.
n
(mathematics) A nonempty set R that supports hyperaddition as an abelian hypergroup with neutral element 0, multiplication as a monoid with identity element one, supports the distributive law, and for which multiplication by zero always yields the result 0.
n
(mathematics) The subset of a codomain comprising those elements that are images of something.
n
(mathematics) The theorem that any closed, orientable, connected 3-manifold may be obtained by performing Dehn surgery on a framed link in the 3-sphere with ±1 surgery coefficients, and that each component of the link can be assumed to be unknotted.
n
(algebra) A matrix ring over a commutative ring.
n
(algebra, ring theory) An abelian group equipped with the operation of multiplication by an element of a ring (or another of certain algebraic objects), representing a generalisation of the concept of vector space with scalar multiplication.
n
(mathematics) A certain type of left-invariant metric on a nilpotent Lie group.
n
(mathematics) A supergroup.
n
(algebra, field theory, of a finite field) An element that generates the multiplicative group of a given Galois field (finite field).
n
(linear algebra) Multiplication of a vector by a scalar (which belongs to the vector space's field of scalars).
adj
(mathematics) Describing a generalization of a semisimple ring
n
(mathematics) Synonym of hyperparameter
adj
(algebra, of a group action) Such that, for any two elements of the acted-upon set, some group element maps the first to the second.
n
(mathematics) A quotient of the direct product of a family of structures
adj
(mathematics, of a category) in which each object has only a set of pairwise nonisomorphic subobjects
n
(group theory) A group element, expressed as a product of group elements.
n
A generalization of the zero vector to tensor space.
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