Characterizations of intra-regular gamma AG-groupoids by the properties of their gamma ideals

TL;DR

This paper characterizes intra-regular gamma AG-groupoids by examining properties of their gamma ideals, proving their equivalence and idempotency, and generalizing existing results in the algebraic structure.

Contribution

It introduces new characterizations of intra-regular gamma AG-groupoids based on properties of various gamma ideals and generalizes previous results in the field.

Findings

All gamma-ideals coincide in intra-regular gamma AG^{**}-groupoids.

All gamma-ideals are gamma-idempotent in these structures.

The paper generalizes existing results on gamma-ideals in gamma AG-groupoids.

Abstract

We have characterized an intra-regular {\Gamma}-AG^{**}-groupoids by using the properties of {\Gamma}-ideals (left, right, two-sided ), {\Gamma}-interior, {\Gamma}-quasi, {\Gamma}-bi and {\Gamma}-generalized bi and {\Gamma}-(1,2)). We have prove that all the {\Gamma}-ideals coincides in an intra-regular {\Gamma}-AG^{**}-groupoids. It has been examined that all the {\Gamma}-ideals of an intra-regular {\Gamma}-AG^{**}-groupoids are {\Gamma}-idempotent. In this paper we define all {\Gamma}-ideals in {\Gamma}-AG^{**}-groupoids and we generalize some results.