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On basic properties of relative Γ-ideals in Γ-near rings

Department of Natural and Applied Sciences, Glocal University, Mirzapur,saharanpur, U. P., India.

Department of Mathematics, Jamia Millia Islamia, New Delhi, India.

Department of Mathematics, Acharya Nagarjuna University, A. P., India.

Department of School Education, Kashmir, India

* Corresponding Author
Annals of Communications in Mathematics 2021
, 4 (3),
278-283.
https://doi.org/10.62072/acm.2021.040307
Received: 18 November 2021 |
Accepted: 27 December 2021 |
Published: 31 December 2021

Abstract

The algebraic system Γ-near rings was introduced by Satyanarayana. Tamizh and Ganesan introduced the concept of bi-ideals in near-rings [On bi-ideals of near-rings, Indian J. Pure Appl. Math., 18(11), 1002-1005(1987)]. Tamizh and Meenakumari defined the concept of bi-ideals in Γ-near-rings and characterized Γ-near-fields [Bi-Ideals of Gamma Near-Rings, Southeast Asian Bulletin of Mathematics(2004), 27: 983-988]. Satyanarayana, Yahya, Basar and Kuncham studied abstract affine Γ-nearrings [Some Results on Abstract Affine Gamma-Near-Rings, International Journal of Pure and Applied Mathematical Sciences, 7(1) (2014), 43-49]. Recently, Basar, Satyanarayana, Kuncham, Kumar and Yahya studied some relative ideals in Γ-nearrings [A note on relative Γ-ideals in abstract affine Γ-nearrings, GIS Science Journal, 8(10)(2021), 9-13]. In this paper, we study relative quasi-Γ-ideals and relative bi-Γ-ideals in Γ-near rings. We also proved nice characterizations of Γ-near rings by these basic relative Γ-ideals.

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Cite This Article

On basic properties of relative Γ-ideals in Γ-near rings.

Annals of Communications in Mathematics,

2021,
4 (3):
278-283.
https://doi.org/10.62072/acm.2021.040307
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  • Copyright (c) 2023 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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