Cancellative Left (Right) Regular Semigroups

Abstract

Abstract.A semigroup S is called regular semigroup if for every a ∈ S there exists x in S such that axa = a introduced by J. A. Green. In this paper, some preliminaries and basic concept of regular semigroups were presented. And proved that a cancellative semigroup S is left(right) regular semigroup if and only if it is a: (i) completely regular semigroup (ii) Clifford semigroup (iii) E-inversive semigroup (iv) -regular semigroup.