Idempotent ordered semigroup

Abstract

An element e of an ordered semigroup $(S,\cdot ,\le )$ is called an ordered idempotent if $e\le e^2$. We call an ordered semigroup $S$ idempotent ordered semigroup if every element of $S$ is an ordered idempotent. Every idempotent semigroup is a complete semilattice of rectangular idempotent semigroups and in this way we arrive to many other important classes of idempotent ordered semigroups.

10 pages, 1 figure