On completely regular and strongly regular ordered $\Gamma$-semigroups

TL;DR

This paper explores the extension of properties from ordered semigroups to ordered $ ext{Gamma}$-semigroups, introducing the concept of strongly regular $po$-$ ext{Gamma}$-semigroups and providing their characterization.

Contribution

It introduces the concept of strongly regular $po$-$ ext{Gamma}$-semigroups and offers a characterization, bridging results from ordered semigroups to $ ext{Gamma}$-semigroups.

Findings

Introduction of strongly regular $po$-$ ext{Gamma}$-semigroups

Characterization of these semigroups

Transfer of results from ordered semigroups

Abstract

Our aim is to show the way we pass from the results of ordered semigroups (or semigroups) to ordered $\Gamma$-semigroups (or $\Gamma$-semigroups). The results of this note have been transferred from ordered semigroups. The concept of strongly regular $po$-$\Gamma$-semigroups has been first introduced here and a characterization of strongly regular $po$-$\Gamma$-semigroups is given.