On the structure of completely inverse AG**-groupoids

TL;DR

This paper explores the algebraic structure of completely inverse AG**-groupoids, revealing their composition as semilattices of abelian groups and analyzing their automorphisms that fix idempotents.

Contribution

It characterizes the structure of completely inverse AG**-groupoids in terms of semilattices of abelian groups and their automorphisms, providing new insights into their algebraic properties.

Findings

Structure described as semilattices of abelian groups

Automorphisms are involutive and fix idempotents

Provides a classification framework for these groupoids

Abstract

We determine the structure of completely inverse AG**-groupoids modulo semilattices of abelian groups and their involutive, idempotent-fixed automorphisms.