SANDWICH SETS AND CONGRUENCES IN COMPLETELY INVERSE \(AG^{∗∗}\)-GROUPOIDS

Abstract

In this paper, we investigate sandwich set in a completely inverse AG^∗∗-groupoid and make use of it for congruence pairs of a completely inverse AG^∗∗-groupoid.  We discuss completely inverse AG^∗∗-groupoids in terms of partial order and show that the natural partial order is an equality relation in an AG-group.  Further, we study idempotent-separating and idempotent-pure congruences on completely inverse AG^∗∗-groupoids and show that the quotient structure for a maximum idempotent-separating congruence on an AG^∗∗-groupoid is fundamental.  Further, we characterize E-unitary completely inverse AG^∗∗-groupoids and provide a condition for a compatibility relation to be transitive.