nLab commutative semigroup

Definition

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

$$x \cdot y = y \cdot x \,.$$

Examples

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

Related concepts

• semigroup (noncommutative version)

• commutative invertible semigroup (invertible version)

• commutative monoid (unital version)

• commutative magma (non-associative version)