On Cyclic Associative Abel-Grassman Groupoids

M. Iqbal; I. Ahmad; M. Shah; M. Irfan Ali

doi:10.9734/BJMCS/2016/21867

Research Article Open access CC BY 4.0

On Cyclic Associative Abel-Grassman Groupoids

M. Iqbal, I. Ahmad, M. Shah, M. Irfan Ali

Journal of Advances in Mathematics and Computer Science · pp. 1–16 · Published 7 Nov 2015

10.9734/BJMCS/2016/21867

Abstract

A new subclass of AG-groupoids, so called, cyclic associative Abel-Grassman groupoids or CA- AG-groupoid is studied. These have been enumerated up to order 6. A test for the verification of cyclic associativity for an arbitrary AG-groupoid has been introduced. Various properties of CA- AG-groupoids have been studied. Relationship among CA-AG-groupoids and other subclasses of AG-groupoids is investigated. It is shown that the subclass of CA-AG-groupoid is di erent from that of the AG*-groupoid as well as AG**-groupoids.

AG-groupoid cyclic associativity CA-AG-groupoid CA-test Nuclear square right alternative bi-commutative paramedial AG-groupoids.

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M. Iqbal, I. Ahmad, M. Shah, M. Irfan Ali (2015). On Cyclic Associative Abel-Grassman Groupoids. Journal of Advances in Mathematics and Computer Science , 1–16. https://doi.org/10.9734/BJMCS/2016/21867

Affiliations

M. Iqbal — Department of Mathematics, University of Malakand, Chakdara, Pakistan.
I. Ahmad — Department of Mathematics, University of Malakand, Chakdara, Pakistan.
M. Shah — Department of Mathematics, Govt. Post Graduate College Mardan, Pakistan.
M. Irfan Ali — Federal Government College for Girls F-7, Islamabad, Pakistan.

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