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276883

Endo-Noetherian Skew Generalized Power Series Rings

Article

Last updated: 28 Dec 2024

Subjects

-

Tags

Mathematics and Computer Science

Abstract

Endo-Noetherian modules were introduced by A. Kaidi and E. Sanchez] as a generalization of Noetherian modules. A left Ɍ-module M which satisfies the ascending chain condition for endomorphic kernels is said to be endo-Noetherian. A ring Ɍ is left endo-Noetherian if Ɍ over itself as a left module is endo-Noetherian. The property of endo-Noetherian were studied for the polynomial ring Ɍ[x] and the formal power series ring Ɍ[[x]]. Throughout this article, we are interested in the study of the left endo-Noetherian property of the skew generalized power series ring Ɍ[[ℵ, σ]], we show under what conditions on a ring Ɍ, a strictly ordered monoid (ℵ, ≼), and a monoid homomorphism σ: ℵ ⟶ End (Ɍ), the skew generalized power series ring Ɍ[[ℵ, σ]] is left endo-Noetherian if and only if Ɍ is left endo-Noetherian. We find new corollaries on generalized power series rings, power series rings, and polynomial rings as special examples of our general conclusion.

DOI

10.21608/aunj.2022.154297.1032

Keywords

Endo-Noetherian rings, Skew generalized power series rings, (ℵ, σ)- Armendariz rings

Authors

First Name

Neamat

Last Name

Mohamed

MiddleName

Abdelnasser

Affiliation

Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt.

Email

neamanasser7@gmail.com

City

-

Orcid

-

First Name

Refaat

Last Name

Salem

MiddleName

Mohamed

Affiliation

Mathematics Department, Faculty of Science, Al-Azhar University, Cairo, Egypt

Email

rsalem_02@hotmail.com

City

Cairo

Orcid

-

First Name

Ramy

Last Name

Abdel-Khaleq

MiddleName

El-Sayed

Affiliation

Mathematics Department, Faculty of Science, Al-Azhar University, Cairo, Egypt

Email

ramy_ama@yahoo.com

City

Cairo

Orcid

-

Volume

52

Article Issue

1

Related Issue

38469

Issue Date

2023-01-01

Receive Date

2022-08-04

Publish Date

2023-01-01

Page Start

13

Page End

22

Print ISSN

2812-5029

Online ISSN

2812-5037

Link

https://aunj.journals.ekb.eg/article_276883.html

Detail API

https://aunj.journals.ekb.eg/service?article_code=276883

Order

276,883

Type

Novel Research Articles

Type Code

2,242

Publication Type

Journal

Publication Title

Assiut University Journal of Multidisciplinary Scientific Research

Publication Link

https://aunj.journals.ekb.eg/

MainTitle

Endo-Noetherian Skew Generalized Power Series Rings

Details

Type

Article

Created At

23 Jan 2023