Definition:Commutative Semigroup
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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.
Sources
- Seth Warner: Modern Algebra (1965)... (previous)... (next): $\S 7$
- Thomas A. Whitelaw: An Introduction to Abstract Algebra (1978)... (previous)... (next): $\S 29$
