Finite AG-groupoid with left identity and left zero

Qaiser Mushtaq and M. S. Kamran

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 27, 1-3

Abstract:

A groupoid G whose elements satisfy the left invertive law: ( a b ) c = ( c b ) a is known as Abel-Grassman's groupoid (AG-groupoid). It is a nonassociative algebraic structure midway between a groupoid and a commutative semigroup. In this note, we show that if G is a finite AG-groupoid with a left zero then, under certain conditions, G without the left zero element is a commutative group.

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:620512

DOI: 10.1155/S0161171201010997

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