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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2507.23668 |
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| _version_ | 1866918108669673472 |
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| author | Salem, R. M. Abdel-Khalek, R. E. Abdelnasser, N. |
| author_facet | Salem, R. M. Abdel-Khalek, R. E. Abdelnasser, N. |
| contents | In this article, we proceed on the transfer of the left endo-Noetherian property on certain ring extensions. We transfer of the right (left) endo-Noetherian property to the right (left) quotient rings. For a subring $T$ of $R$ and a finite set of indeterminates $X$, we prove that $T + XR[[X]]$ is left endo-Noetherian if and only if $R[[X]]$ is left endo-Noetherian. In addition, we prove that the subring $Λ:=\{ f \in R[[S,ω]]: f(1) \in T \}$ of the skew generalized power series ring $R[[S, ω]]$ is left endo-Noetherian if and only if $R[[S, ω]]$ is left endo-Noetherian. Also, we study the left endo-Noetherian property over the amalgamated duplication rings $R \bowtie I$ and $ R \bowtie ^f J$. Finally, we introduce additional results on left endo-Noetherian rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23668 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some Extensions of Endo-Noetherian Rings Salem, R. M. Abdel-Khalek, R. E. Abdelnasser, N. Rings and Algebras In this article, we proceed on the transfer of the left endo-Noetherian property on certain ring extensions. We transfer of the right (left) endo-Noetherian property to the right (left) quotient rings. For a subring $T$ of $R$ and a finite set of indeterminates $X$, we prove that $T + XR[[X]]$ is left endo-Noetherian if and only if $R[[X]]$ is left endo-Noetherian. In addition, we prove that the subring $Λ:=\{ f \in R[[S,ω]]: f(1) \in T \}$ of the skew generalized power series ring $R[[S, ω]]$ is left endo-Noetherian if and only if $R[[S, ω]]$ is left endo-Noetherian. Also, we study the left endo-Noetherian property over the amalgamated duplication rings $R \bowtie I$ and $ R \bowtie ^f J$. Finally, we introduce additional results on left endo-Noetherian rings. |
| title | Some Extensions of Endo-Noetherian Rings |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2507.23668 |