On classes of E-inversive semigroups and semigroups whose idempotents form a subsemigroup

摘要

A semigroup S is called E-inversive if for every a c S there is an x c S such that ax is idempotent. The purpose of this paper is the investigation of E-inversive semigroups and sernigroups whose idempotents form a subsemigroup. Basic properties are analysed and, in particular, semigroups whose idempotents form a semilattice or a rectangular band are considered. To provide examples and characterizations, the construction methods of generalized Rees matrix sernigroups and semidirect products are employed.