Definition:Commutative Semigroup

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.