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arXiv · 1010.5965

On some classes of Abel-Grassmann's groupoids

Madad Khan·Faisal·Venus Amjid
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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.

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Madad Khan, Faisal, Venus Amjid. 2010-10-28. On some classes of Abel-Grassmann's groupoids. https://arxiv.org/abs/1010.5965

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