Congruences on E-Inversive Semigroups
Y. L. Anasuya · Thai Journal of Mathematics · 2012
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.