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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.
Muhammad Iqbal, Imtiaz Ahmad. (2019) Some Congruences on CA-AG-groupoids, , Volume 51, Issue 3.
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