On S-J-Noetherian Rings
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911324022243328 |
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| author | Singh, Tushar Ansari, Ajim Uddin Kumar, Shiv Datt |
| author_facet | Singh, Tushar Ansari, Ajim Uddin Kumar, Shiv Datt |
| contents | Let $R$ be a commutative ring with identity, $S\subseteq R$ be a multiplicative set and $J$ be an ideal of $R$. In this paper, we introduce the concept of $S$-$J$-Noetherian rings, which generalizes both $J$-Noetherian rings and $S$-Noetherian rings. We study several properties and charaterizations of this new class of rings. For instance, we prove Cohen's-type theorem for $S$-$J$-Noetherian rings. Among other results, we establish the existence of $S$-primary decomposition in $S$-$J$-Noetherian rings as a generalization of classical Lasker-Noether theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15078 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On S-J-Noetherian Rings Singh, Tushar Ansari, Ajim Uddin Kumar, Shiv Datt Commutative Algebra J-ideals, S-J-Noetherian rings, S-Noetherian rings Let $R$ be a commutative ring with identity, $S\subseteq R$ be a multiplicative set and $J$ be an ideal of $R$. In this paper, we introduce the concept of $S$-$J$-Noetherian rings, which generalizes both $J$-Noetherian rings and $S$-Noetherian rings. We study several properties and charaterizations of this new class of rings. For instance, we prove Cohen's-type theorem for $S$-$J$-Noetherian rings. Among other results, we establish the existence of $S$-primary decomposition in $S$-$J$-Noetherian rings as a generalization of classical Lasker-Noether theorem. |
| title | On S-J-Noetherian Rings |
| topic | Commutative Algebra J-ideals, S-J-Noetherian rings, S-Noetherian rings |
| url | https://arxiv.org/abs/2512.15078 |