# Definition:Commutative Semigroup

## Contents

## 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

- Results about
**commutative semigroups**can be found here.

## Sources

- 1965: Seth Warner:
*Modern Algebra*... (previous) ... (next): $\S 7$ - 1978: Thomas A. Whitelaw:
*An Introduction to Abstract Algebra*... (previous) ... (next): $\S 29$. Semigroups: definition and examples