Decomposition of Stein AG-groupoid via congruence relations

Abstract

The In this paper, we examine the class of Stein AG-groupoids S, establishing some features in terms of powers and exploring some basic aspects of elements. We demonstrate the associative properties of S. powers without the additional left identity, weak associative laws, and local associativity requirements seen in other AG-groupoids subclasses such as AG^(**), LAD, RAD, and Cheban AG-groupoids. We establish the following relations on S: ζ, ξ, ϕ, and β. We also demonstrate the equivalence of the relations ξ,ϕ. Additionally, we demonstrate that the S/ζ is a maximal separative commutative image of S that is also anti-separative. Furthermore, the maximal separative commutative image of S is S/ϕ.