commutative group
1commutative group — noun a group that satisfies the commutative law • Syn: ↑Abelian group • Hypernyms: ↑group, ↑mathematical group …
2Commutative property — For other uses, see Commute (disambiguation). In mathematics an operation is commutative if changing the order of the operands does not change the end result. It is a fundamental property of many binary operations, and many mathematical proofs… …
3Group ring — This page discusses the algebraic group ring of a discrete group; for the case of a topological group see group algebra, and for a general group see Group Hopf algebra. In algebra, a group ring is a free module and at the same time a ring,… …
4Group scheme — In mathematics, a group scheme is a group object in the category of schemes. That is, it is a scheme G with the equivalent properties* there is a group law expressible as a multiplication μ and inversion map ι on G ; or * G is a functor (as in… …
5commutative — adjective Date: 1612 1. of, relating to, or showing commutation 2. of, relating to, having, or being the property that a given mathematical operation and set have when the result obtained using any two elements of the set with the operation does… …
6Commutative ring — In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra. Some specific kinds of commutative rings are given with …
7group theory — the branch of mathematics that deals with the structure of mathematical groups and mappings between them. [1895 1900] * * * In modern algebra, a system consisting of a set of elements and an operation for combining the elements, which together… …
8Group representation — In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group… …
9Group homomorphism — In mathematics, given two groups ( G , *) and ( H , ·), a group homomorphism from ( G , *) to ( H , ·) is a function h : G → H such that for all u and v in G it holds that: h(u*v) = h(u) h(v) where the group operation on the left hand side of the …
10commutative — [kə mju:tətɪv, kɒmjʊˌtətɪv] adjective Mathematics involving the condition that a group of quantities connected by operators gives the same result whatever the order of the quantities involved, e.g. a × b = b × a …
