Acta Mathematica Sinica, English Series

, Volume 29, Issue 3, pp 609–624

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

Authors

    • Department of Mathematics and Computer Science, Faculty of Natural SciencesUniversity of Gjirokastra
  • Jani Dine
    • Department of Mathematics and Computer Science, Faculty of Natural SciencesUniversity of Gjirokastra
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
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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-semigroupGreen’s relation(m, n)0-regular Γ-semigroup20-regular Γ-semigroupcompletely 0-simpleabsorbency0-minimal left (right, quasi)-ideal

MR(2000) Subject Classification

20M1020M1220M17

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