Endo-Noetherian Skew Generalized Power Series Rings | ||||
| Assiut University Journal of Multidisciplinary Scientific Research | ||||
| Volume 52, Issue 1, January 2023, Page 13-22 PDF (733.22 K) | ||||
| Document Type: Novel Research Articles | ||||
| DOI: 10.21608/aunj.2022.154297.1032 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
Neamat Abdelnasser Mohamed  1; Refaat Mohamed Salem2; Ramy El-Sayed Abdel-Khaleq2
| ||||
| 1Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt. | ||||
| 2Mathematics Department, Faculty of Science, Al-Azhar University, Cairo, Egypt | ||||
| 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. | ||||
| Keywords | ||||
| Endo-Noetherian rings; Skew generalized power series rings; (ℵ, σ)- Armendariz rings | ||||
|
Statistics Article View: 197 PDF Download: 253 |
||||
