nLab commutative semigroup

Contents

Contents

Definition

A semigroup (S,)(S,\cdot) is called commutative if its binary operation ()():S×S(-)\cdot(-) \colon S \times S has the property that for all x,ySx,y \in S then

xy=yx. x \cdot y = y \cdot x \,.

Examples

Examples include commutative monoids, abelian groups, commutative rings, commutative algebras etc.

Created on August 3, 2022 at 18:27:12. See the history of this page for a list of all contributions to it.