A Study of Anti-rectangular AG-groupoids

Abstract

An AG-groupoid H satisfying the rule of left semisymmetry, (ab)a = b for all a, b ∈ H is called an anti-rectangular AG-groupoid. This article is devoted to the study of various characterizations of antirectangular AG-groupoids and to the relations of this subclass with various subclasses of AG-groupoids and with other algebraic structures such as semigroups, commutative semigroups, monoids, abelian groups, etc. Furthermore, we remove the miss conception about the proper ideals of anti-rectangular AG-groupoids in [20] by proving that it is simple