On neutrosophic ideals and prime ideals in rings

Ali Yahya Hummdi; Amr Elrawy; Ali Yahya Hummdi; Amr Elrawy

doi:10.3934/math.20241205

AIMS Mathematics

2024, Volume 9, Issue 9: 24762-24775. doi: 10.3934/math.20241205

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Research article

On neutrosophic ideals and prime ideals in rings

Ali Yahya Hummdi ¹,
Amr Elrawy ^{2
,
,}

1.
Department of Mathematics, King Khalid University, Abha 61471, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, SVU, Qena 83523, Egypt

Received: 17 May 2024 Revised: 16 August 2024 Accepted: 19 August 2024 Published: 23 August 2024
MSC : 08A72, 11R44, 13A15

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 $ \mathbb{Z} $.
- neutrosophic set,
- regular ring,
- neutrosophic ideal,
- neutrosophic prime ideal
Citation: Ali Yahya Hummdi, Amr Elrawy. On neutrosophic ideals and prime ideals in rings[J]. AIMS Mathematics, 2024, 9(9): 24762-24775. doi: 10.3934/math.20241205

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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 $ \mathbb{Z} $.

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