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Regularity Based Characterizations of Le-Γ-semigroups

1Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia2Department of Mathematics and Statistics, School of Applied Science and Humanities, Vignan’s Foundation for Science, Technology and Research, Vadlamudi, Guntur-522213, AP, India3Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia4Department of Statistics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia
* Corresponding Author: G. Muhiuddin. Email: chishtygm@gmail.com

Annals of Communications in Mathematics 2024, 7 (4), 354-365. https://doi.org/10.62072/acm.2024.070403
Received: 24 Sept 2024 |
Accepted: 24 Nov 2024 |
Published: 31 Dec 2024

Abstract

This article provides an in-depth examination of (m, n, γ)-regular le-Γ- semigroups, focusing on the characterization and properties of various types of ideal el- ements within these structures. Specifically, the discussion encompasses (m, n, γ)-ideal elements, (m, 0, γ)-ideal elements, and (0, n, γ)-ideal elements, highlighting their sig- nificance and interrelationships. Furthermore, the article investigates the (m, n, α, β)- regularity associated with the set denoted as I(m,n,α,β), which consists of all (m, n, α, β)- ideal elements. In conjunction, the study explores the set Q(m,n,α,β), which comprises all (m, n, α, β)-quasi-ideal elements of le-Γ-semigroups, detailing the implications of these classifications on the structure and behavior of the semigroups. Additionally, the research delves into the concept of 0-minimality, particularly concerning (0, m, γ)-ideal elements in both poe-Γ-semigroups and le-Γ-semigroups. This aspect of the study aims to clarify the foundational properties of ideal elements and their roles in the broader context of semi- group theory. The findings presented in this article contribute to a deeper understanding of the algebraic properties of le-Γ-semigroups and their ideal elements, paving the way for future research in this area.

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Cite This Article

G. Muhiuddin, Ahsan Mahboob, Montaser Saudi Ali, Elsiddig Idriss Mohamed.
Regularity Based Characterizations of Le-Γ-semigroups.
Annals of Communications in Mathematics
2024,
7 (4):
354-365.
https://doi.org/10.62072/acm.2024.070403

Creative Commons License
Copyright © 2024 by the Author(s). Licensee Techno Sky Publications. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

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