Semigroups whose idempotents form a subsemigroup ∗

We prove that every semigroup S in which the idempotents form a sub-semigroup 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. * The authors gratefully acknowledge support from the Working Group ASMICS of the European Community program ESPRIT (EBRA 3166).