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ArticleOriginal scientific text

Title

Characterizations of ordered Γ-Abel-Grassmann's groupoids

Authors 1, 1, 2, 3

Affiliations

  1. Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan
  2. Department of Mathematics, University of Malakand, Chakdara, Pakistan
  3. Department of Mathematics,, Quaid-i-Azam University, Islamabad, Pakistan

Abstract

In this paper, we introduced the concept of ordered Γ-AG-groupoids, Γ-ideals and some classes in ordered Γ-AG-groupoids. We have shown that every Γ-ideal in an ordered Γ-AG**-groupoid S is Γ-prime if and only if it is Γ-idempotent and the set of Γ-ideals of S is Γ-totally ordered under inclusion. We have proved that the set of Γ-ideals of S form a semilattice, also we have investigated some classes of ordered Γ-AG**-groupoid and it has shown that weakly regular, intra-regular, right regular, left regular, left quasi regular, completely regular and (2,2)-regular ordered Γ-AG**-groupoids coincide. Further we have proved that every intra-regular ordered Γ-AG**-groupoid is regular but the converse is not true in general. Furthermore we have shown that non-associative regular, weakly regular, intra-regular, right regular, left regular, left quasi regular, completely regular, (2,2)-regular and strongly regular Γ-AG*-groupoids do not exist.

Keywords

ENG
ordered Γ-AG-groupoids, Γ-ideals, regular Γ-AG**-groupoids

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Discussiones Mathematicae - General Algebra and Applications
2014/34/1
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Pages:
55-73
Main language of publication
English
Received
2013-08-09
Accepted
2014-01-24
Published
2014

DOI: 10.7151/dmgaa.1217

Exact and natural sciences