commutative semigroup

A semigroup $S$ is commutative if the defining binary operation is commutative (http://planetmath.org/Commutative). That is, for all $x,y\in S$ , the identity $xy=yx$ holds.

Although the term Abelian semigroup is sometimes used, it is more common simply to refer to such semigroups as commutative semigroups.

A monoid which is also a commutative semigroup is called a commutative monoid.