  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 \in G
(that is, ea = a for all a \in G) and for all a \in G there exists a' \in G
such that a.a' = a'.a = e. In this article we introduce the concept of
AG-groupoids (mod n) and AG-group (mod n) using Vasantha's constructions [1].
This enables us to prove that AG-groupoids (mod n) and AG-groups (mod n) exist
for every integer n \geq 3. We also give some nice characterizations of some
classes of AG-groupoids in terms of AG-groupoids (mod n).
