Article

Acta Mathematica Sinica, English Series

, Volume 29, Issue 3, pp 609-624

On Green’s relations, 20-regularity and quasi-ideals in Γ-semigroups

  • Kostaq HilaAffiliated withDepartment of Mathematics and Computer Science, Faculty of Natural Sciences, University of Gjirokastra Email author 
  • , Jani DineAffiliated withDepartment of Mathematics and Computer Science, Faculty of Natural Sciences, University of Gjirokastra

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Abstract

In this paper, we introduce the definition of (m, n)0-regularity in Γ-semigroups. We investigate and characterize the 20-regular class of Γ-semigroups using Green’s relations. Extending and generalizing the Croisot’s Theory of Decomposition for Γ-semigroups, we introduce and study the absorbent and regular absorbent Γ-semigroups. We approach this problem by examining quasi-ideals using Green’s relations.

Keywords

Γ-semigroup Green’s relation (m, n)0-regular Γ-semigroup 20-regular Γ-semigroup completely 0-simple absorbency 0-minimal left (right, quasi)-ideal

MR(2000) Subject Classification

20M10 20M12 20M17