On Cyclic Associative Abel-Grassman Groupoids
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.
*Author to whom correspondence should be addressed.
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.
Keywords: AG-groupoid, cyclic associativity, CA-AG-groupoid, CA-test, Nuclear square, right alternative, bi-commutative, paramedial AG-groupoids.