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Research Article | Open Access

On neutrosophic ideals and prime ideals in rings

Ali Yahya Hummdi1, Amr Elrawy2( )
Department of Mathematics, King Khalid University, Abha 61471, Saudi Arabia
Department of Mathematics, Faculty of Science, SVU, Qena 83523, Egypt
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Abstract

This article aims to introduce and explore the concept of neutrosophic ideals in the context of rings. Besides, we investigate how the property of regularity in a ring can be understood through the lens of neutrosophic ideals. We further present the concept of neutrosophic prime ideals and systematically identify all neutrosophic prime ideals in Z.

Keywords

neutrosophic setregular ringneutrosophic idealneutrosophic prime ideal
CLC number: 08A72, 11R44, 13A15

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AIMS Mathematics
Volume 9 Issue 9,
September 2024
Pages 24762-24775
DOI: 10.3934/math.20241205

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Cite this article:
Hummdi AY, Elrawy A. On neutrosophic ideals and prime ideals in rings. AIMS Mathematics, 2024, 9(9): 24762-24775. https://doi.org/10.3934/math.20241205

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Received: 17 May 2024
Revised: 16 August 2024
Accepted: 19 August 2024
Published: 15 September 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)