Definition:Commutative Semigroup

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

Then $\left({S, \circ}\right)$ is a commutative semigroup.

Also known as
Some authors refer to a commutative semigroup as an abelian semigroup.

However, the term abelian is usually reserved for commutative groups.