Definition:Commutative Semigroup

Definition

Let $\left({S, \circ}\right)$ be a semigroup such that the operation $\circ$ is a commutative operation.

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.

Also see

• Definition:Commutative Magma
• Definition:Commutative Monoid
• Definition:Abelian Group

• Results about commutative semigroups can be found here.

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 7$: Semigroups and Groups
• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 29$. Semigroups: definition and examples