Definition:Idempotent Semigroup

Definition
An idempotent semigroup is a semigroup whose operation is idempotent.

That is, a semigroup $\left({S, \circ}\right)$ is idempotent :


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

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

 * Definition:Semilattice (Abstract Algebra)