Acta Mathematica Sinica, English Series

, Volume 29, Issue 3, pp 609–624

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

Article

DOI: 10.1007/s10114-012-0027-1

Cite this article as:
Hila, K. & Dine, J. Acta. Math. Sin.-English Ser. (2013) 29: 609. doi:10.1007/s10114-012-0027-1
  • 121 Downloads

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 

Supplementary material

10114_2012_27_MOESM1_ESM.tex (62 kb)
Supplementary material, approximately 62.4 KB.

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

Personalised recommendations