Some aspects in Noetherian modules and rings

Nasr Anwer Zeyada; Makkiah S. Makki; Nasr Anwer Zeyada; Makkiah S. Makki

doi:10.3934/math.2022935

AIMS Mathematics

2022, Volume 7, Issue 9: 17019-17025. doi: 10.3934/math.2022935

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Research article

Some aspects in Noetherian modules and rings

Nasr Anwer Zeyada ^{1,2
,
,},
Makkiah S. Makki ³

1.
Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
2.
Department of Mathematics, College of Science, University of Jeddah, Jeddah 23218, Saudi Arabia
3.
Department of Mathematical Sciences, Faculty of Applied Sciences, Umm Alqura University, Makkah 21955, Saudi Arabia

Received: 04 May 2022 Revised: 26 June 2022 Accepted: 30 June 2022 Published: 19 July 2022
MSC : 16D50, 16L30, 16L60, 16P20

Many authors have focused on the concept of Noetherian rings. M. Kosan and T. Quynh recently published an article on the Noetherian ring's new properties and their relation to the direct sum of injective hulls of simple right modules and essential extensions. Throughout this article, we extend the results of M. Kosan and T. Quynh to simple singular right modules and strongly singular injectivity.
- Noetherian ring,
- singular modules
Citation: Nasr Anwer Zeyada, Makkiah S. Makki. Some aspects in Noetherian modules and rings[J]. AIMS Mathematics, 2022, 7(9): 17019-17025. doi: 10.3934/math.2022935

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Abstract

Many authors have focused on the concept of Noetherian rings. M. Kosan and T. Quynh recently published an article on the Noetherian ring's new properties and their relation to the direct sum of injective hulls of simple right modules and essential extensions. Throughout this article, we extend the results of M. Kosan and T. Quynh to simple singular right modules and strongly singular injectivity.

References

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