Some characterizations of regularity and intra-regularity of $\Gamma$-semigroups by means of quasi-ideals

Abstract

The concept of regularity in Γ-semigroups is not very easy to deal with even though it shares some analogy with its analogue of semigroup theory. In this paper we establish a mechanism which translates the regularity in a Γ-semigroup (S,Γ) as the usual von Neumann regularity in an ordinary semigroup Ωγ0 that we construct in terms of (S,Γ). This enables us to characterize the regularity in Γ-semigroups by means of quasi-ideals. A similar characterization is proved for those Γ-semigroups which are regular and intra-regular. AMS Mathematics Subject Classification (2010): 20M05, 20M10, 20M12, 20M17