On Classes of E-Inversive Semigroups and Semigroups Whose Idempotents Form a Subsemigroup

Abstract

A semigroup S is called E-inversive if for every a ∈ S there is an x ∈ S such that ax is idempotent. The purpose of this paper is the investigation of E-inversive semigroups and semigroups 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 semigroups and semidirect products are employed.

Key Word:

• E-inversive semigroups

2000 Mathematics Subject Classification:

• 20M10

Acknowledgments

Notes

^#Communicated by D. Easdown.

^†This paper is part of the author's doctoral thesis written at the University of Vienna under the direction of Professor H. Mitsch.