A semigroup $S$ is commutative if the defining binary operation is 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.