Acta Mathematica Sinica, English Series

, Volume 29, Issue 3, pp 609–624 | Cite as

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

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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 

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of Mathematics and Computer Science, Faculty of Natural SciencesUniversity of GjirokastraGjirokastraAlbania

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