Definition:Idempotent Semigroup

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An idempotent semigroup is a semigroup whose operation is idempotent.

That is, a semigroup $\struct {S, \circ}$ is idempotent if and only if:

$\forall x \in S: x \circ x = x$

Also known as

There are extensive bodies of research covering idempotent semigroups.

In this literature, band is a common synonym for idempotent semigroup.

Also see