Congruences on E-Inversive Semigroups

Yeeranki Lakshmi Anasuya

Abstract

A semigroup S is said to be E-inversive if for each a ∈ S there exists x ∈ S such that ax is an idempotent. In this paper we have obtained a characterization on E-inversive semigroup S in which Reg(S) is completely simple sub semigroup of S. It is also proved that in an orthodox semigroup S if a ≤ b then W(a) ⊆ W(b) and we have given an example for which the converse is not true. Finally in his paper, Certain congruences on E-inversive E-semigroups, the author has obtained regular congruences on an E-inversive semigroup S in which W(a) has maximal element for all a in S. This motivates us to find the smallest regular congruence on an E-inversive semigroup in which each W(a) has greatest element.