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Inferior Semigroups and Ideals

1Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia.2Department of Mathematics Education,Gyeongsang National University, Jinju 660-701, Korea.

* Corresponding Author: G. Muhiuddin. Email: skywine@gmail.com

Annals of Communications in Mathematics 2025, 8 (3), 350-362. https://doi.org/10.62072/acm.2025.080302

Received: 26 June 2025 |

Accepted: 00 September 2025 |

Published:

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ABSTRACT.

Inferior semigroups, left (right) inferior ideals and inferior quasi-ideals in semi-groups are introduced, and several properties are investigated. Characterizations of inferior semigroups and ideals are considered, and relations between inferior semigroups, inferior ideals and inferior quasi-ideals are discussed. Characteristic inferior mappings and inferior products of inferior mappings are introduced. Using these notions, related properties on inferior semigroups, left (right) inferior ideals and inferior quasi-ideals are investigated. A regular semigroup is characterized by an inferior quasi-ideal.

Keywords

characteristic inferior mapping; inferior mapping; inferior product; inferior quasi-ideal; inferior subalgebra; left (right) inferior ideal

Cite This Article

G. Muhiuddin, Young Bae Jun.

Inferior Semigroups and Ideals.

Annals of Communications in Mathematics

2025,

8 (3):

350-362.

https://doi.org/10.62072/acm.2025.080302

Copyright © 2025 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/).