DefinePK

Abstract

A groupoid satisfying the “left invertive law” is called an Abel-Grassmann’s groupoid (or simply AGgroupoid [2]). In literature different names like “left almost semigroup” (LA-semigroup) [3], left invertive groupoid [4] and right modular groupoid [5] has been used by different authors for the said structure. Many properties of AG-groupoids have been studied in [6, 7]. Various aspects of AG-groupoids have been studied in [2, 8 − 14]. In [1,15], we introduced CA-AG-groupoid as a new subclass of AGgroupoid and studies some fundamental properties of it. In the same paper we introduced CA-test for the verification of cyclic associativity for an arbitrary AG-groupoid. We also enumerated CA-AG-groupoids up to order 6 and further classified it into different subclasses.