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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1217,
author = {Madad Khan and Venus Amjid and Gul Zaman and Naveed Yaqoob},
title = {Characterizations of ordered $\Gamma$-Abel-Grassmann's groupoids},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {34},
year = {2014},
pages = {55-73},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1217}
}
Madad Khan; Venus Amjid; Gul Zaman; Naveed Yaqoob. Characterizations of ordered Γ-Abel-Grassmann's groupoids. Discussiones Mathematicae - General Algebra and Applications, Tome 34 (2014) pp. 55-73. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1217/
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