On some classes of Abel-Grassmann's groupoids
Group Theory
2010-11-01 v2
Abstract
In this paper, we have investigated different classes of an AG-groupoid by their structural properties. We have prove that weakly regular, intra-regular, right regular, left regular, left quasi regular and completely regular coincide in an AG-groupoid with left identity and in AG^{**}-groupoid. Further we have prove that every regular (weakly regular, intra-regular, right regular, left regular, left quasi regular, completely regular) AG-groupoid with left identity (AG^{**}-groupoid) is regular but the converse is not true in general. Also it has been shown that non-associative regular, weakly regular, intra-regular, right regular, left regular, left quasi regular and completely regular AG^{*} groupoids do not exist.
Keywords
Cite
@article{arxiv.1010.5965,
title = {On some classes of Abel-Grassmann's groupoids},
author = {Madad Khan and Faisal and Venus Amjid},
journal= {arXiv preprint arXiv:1010.5965},
year = {2010}
}