Definition:Commutative Semigroup
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Definition
Let $\struct {S, \circ}$ be a semigroup such that the operation $\circ$ is a commutative operation.
Then $\struct {S, \circ}$ 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): 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