On j-Artinian Modules Over Commutative Rings
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909926704545792 |
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| author | Erdemir, Dilara Mahdou, Najib Oubouhou, El Houssaine Tekir, Ünsal |
| author_facet | Erdemir, Dilara Mahdou, Najib Oubouhou, El Houssaine Tekir, Ünsal |
| contents | Researchers introduced the notion of j-Artinian rings in [3] and obtained significant results concerning this new class of rings. Motivated by their definition and findings, we extend the study to modules by introducing the concept of j-Artinian modules. Recall from [9] that, if R is a commutative ring with identity, M is an R-module, and j is a submodule of M, then a submodule N of M is called a j-submodule if N \not\subseteq j. We say that M is a j-Artinian R-module if every descending chain of j-submodules becomes stationary. In this paper, we provide a characterization of j-Artinian modules. Moreover, we establish an analogue of Akizuki's theorem in this context and discuss its extension to amalgamated structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21543 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On j-Artinian Modules Over Commutative Rings Erdemir, Dilara Mahdou, Najib Oubouhou, El Houssaine Tekir, Ünsal Commutative Algebra 13C05, 13C60, 16P20 Researchers introduced the notion of j-Artinian rings in [3] and obtained significant results concerning this new class of rings. Motivated by their definition and findings, we extend the study to modules by introducing the concept of j-Artinian modules. Recall from [9] that, if R is a commutative ring with identity, M is an R-module, and j is a submodule of M, then a submodule N of M is called a j-submodule if N \not\subseteq j. We say that M is a j-Artinian R-module if every descending chain of j-submodules becomes stationary. In this paper, we provide a characterization of j-Artinian modules. Moreover, we establish an analogue of Akizuki's theorem in this context and discuss its extension to amalgamated structures. |
| title | On j-Artinian Modules Over Commutative Rings |
| topic | Commutative Algebra 13C05, 13C60, 16P20 |
| url | https://arxiv.org/abs/2511.21543 |