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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 (c) 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/).