On Modulo AG-Groupoids

Abstract

A groupoid G is called an AG-groupoid if it satisfies the left invertive law: (ab)c = (cb)a. An AG-group G, is an AG-groupoid with left identity e 2 G (that is, ea = a for all a 2 G) and for all a 2 G there exists 12 G such that a 1 a = 1 = e. In this article we introduce the concept of AG-groupoids (mod n) and AG-group (mod n) using Vasanthas constructions [1]. This enables us to prove that AG-groupoids (mod n) and AG-groups (mod n) exist for every integer n 3. We also give some nice characterizations of some classes of AG-groupoids in terms of AG-groupoids (mod n).