Left transitive AG-groupoids.

M. Rashad; I. Ahmad; M. Shah; Z. U. A. Khuhro

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Left transitive AG-groupoids.

Author(s)

M. Rashad Department of Mathematics, University of Malakand, Chakdara Dir L, Pakistan

I. Ahmad Department of Mathematics, University of Malakand, Chakdara Dir L, Pakistan

M. Shah Department of Mathematics, University of Malakand, Chakdara Dir L, Pakistan

Z. U. A. Khuhro Department of Mathematics, University of Malakand, Chakdara Dir L, Pakistan

Abstract

An AG-groupoid is an algebraic structure that satisfies the left invertive law: ab×c=cb×a. We prove that the class of left transitive AG-groupoids (AG-groupoids satisfying the identity, ab×ac=bc) coincides with the class of T2-AG-groupoids. We also developed a simple procedure to test whether an arbitrary groupoid is left transitive AG-groupoid or not. Further, we prove that (i) every left transitive AG-groupoid is transitively commutative AG-groupoid. (ii) For left transitive AG-groupoid the properties of flexibility, right alternatively, AG*-groupoid right nuclear square, middle nuclear square and commutative semigroup are equivalent.

Publication Details

Page(s) 547-552

DOI DOI not available

Published Journal: Sindh University Research Journal, Volume: 46, Issue: 4, Year: 2014

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