Definition:Commutative Semigroup

Definition
Let $\left({S, \circ}\right)$ be a semigroup such that the operation $\circ$ is commutative for every pair of elements in $S$, then $\left({S, \circ}\right)$ is a commutative semigroup.

Some authors refer to a commutative semigroup as abelian, but the term abelian is usually reserved for commutative groups.