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A Note on Relative Tri-quasi-Γ-hyperideals of Γ-semihyperring

Department of Mathematics, Ponmana Semmal Puratchi Thalaivar M. G. R Government Arts and Science College, Sirkazhi, Tamil Nadu-609 108, India.

Department of Mathematics, Arignar Anna Government Arts College, Nammakkal, Tamil Nadu-637 002, India.

Research Scholar, Department of Mathematics, Annamalai University, Annamalainagar, Tamil Nadu-608 002, India.

* Corresponding Author

Annals of Communications in Mathematics 2024

, 7 (4),

376-385.

https://doi.org/10.62072/acm.2024.070405

Received: 27 Sept 2024 |

Accepted: 28 Nov 2024 |

Published: 31 Dec 2024

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Abstract

In this paper, we introduce the concept of tri-quasi hyperideal in Γ-semihyperring generalizing the classical ideal, left ideal, right ideal, bi-ideal, quasi ideal, interior ideal, bi-interior ideal, weak interior ideal, bi-quasi ideal, tri-ideal, quasi-interior ideal and bi- quasi-interior ideal of Γ-semihyperring and semiring. Furthermore, charecterizations of Γ-semihyperring, regular Γ-semihyperring and simple Γ-semihyperring with relative tri- quasi hyperideals are provided discussing the characteristics of Γ-semihyperring of relative tri-quasi hyperideals.

Keywords

regular Γ-semihyperring; relative bi-interior hyperideal; relative bi-quasi hyperideal; relative bi-quasi-interior hyperidea; relative quasi hyperideal; relatve interior hyperideal; tri-quasi simple Γ-semihyperring

Cite This Article

A Note on Relative Tri-quasi-Γ-hyperideals of Γ-semihyperring.

Annals of Communications in Mathematics,

2024,

7 (4):

376-385.

https://doi.org/10.62072/acm.2024.070405

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/).