Some Congruences on CA-AG-groupoids

Abstract

An AG-groupoid S satisfying the identity x(yz) = z(xy) for all x, y, z ∈ S is called a CA-AG-groupoid. In this article the notions of equivalence relation and congruence is extended to CA-AG-groupoids and various congruences on CA-AG-groupoid and inverse CA-AG-groupoid are defined and investigated. Furthermore, it is shown that a suitably defined relation ρ on inverse CA-AG-groupoid S is a maximal idempotentseparating congruence, that S/ρ is fundamental and that the semilattice of idempotents of S is isomorphic to the semilattice of idempotents on S/ρ.