Semigroups whose idempotents form a subsemigroup
Jorge Almeida, Jean-Éric Pin, Pascal Weil · Mathematical Proceedings of the Cambridge Philosophical Society · 1992
Abstract We prove that every semigroup S in which the idempotents form a subsemigroup has an E-unitary cover with the same property. Furthermore, if S is E-dense or orthodox, then its cover can be chosen with the same property. Then we describe the structure of E-unitary dense semigroups. Our results generalize Fountain's results on semigroups in which the idempotents commute, and are analogous to those of Birget, Margolis and Rhodes, and of Jones and Szendrei on finite E-semigroups.