Characterizations of {\Gamma}-AG^{**}-groupoids by their {\Gamma}-ideals

TL;DR

This paper explores various types of ideals in {\Gamma}-AG^{**}-groupoids, establishing their properties and structure, and characterizes regular {\Gamma}-AG^{**}-groupoids through their ideals and semilattice formations.

Contribution

It introduces new characterizations of {\Gamma}-AG^{**}-groupoids based on their ideals and proves the semilattice structure of {\Gamma}-ideals in regular cases.

Findings

{\Gamma}-ideals form a semilattice in regular {\Gamma}-AG^{**}-groupoids.

Regular {\Gamma}-AG^{**}-groupoids can be characterized by their left ideals.

Various types of {\Gamma}-ideals are discussed and classified.

Abstract

In this paper we have discusses {\Gamma}-left, {\Gamma}-right, {\Gamma}-bi-, {\Gamma}-quasi-, {\Gamma}-interior and {\Gamma}-ideals in {\Gamma}-AG^{**}-groupoids and regular {\Gamma}-AG^{**}-groupoids. Moreover we have proved that the set of {\Gamma}-ideals in a regular {\Gamma}-AG^{**}-groupoid form a semilattice structure. Also we have characterized a regular {\Gamma}-AG^{**}-groupoid in terms of left ideals.