A new characterization of the weakly Laskerian (FSF) modules
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913929610919936 |
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| author | Fathi, Ali |
| author_facet | Fathi, Ali |
| contents | Let $R$ be a commutative Noetherian ring and $M$ be an $R$-module such that the set of associated prime ideals of the quotient module $M/L$ is finite for all submodules $L$ of $M$. In this paper, it is shown that there is a finitely generated submodule $N$ of $M$ such that the set of associated primes of $M/N$ and the support of $M/N$ are equal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04573 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new characterization of the weakly Laskerian (FSF) modules Fathi, Ali Commutative Algebra 13C05, 13E99 Let $R$ be a commutative Noetherian ring and $M$ be an $R$-module such that the set of associated prime ideals of the quotient module $M/L$ is finite for all submodules $L$ of $M$. In this paper, it is shown that there is a finitely generated submodule $N$ of $M$ such that the set of associated primes of $M/N$ and the support of $M/N$ are equal. |
| title | A new characterization of the weakly Laskerian (FSF) modules |
| topic | Commutative Algebra 13C05, 13E99 |
| url | https://arxiv.org/abs/2507.04573 |