Some new module-theoretic characterizations of $S$-coherent rings
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915064997478400 |
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| author | Zhang, Xiaolei |
| author_facet | Zhang, Xiaolei |
| contents | Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$. In this paper, we first introduce and study the notions of $s$-pure exact sequences and $s$-absolutely pure modules which extend the classical notions of pure exact sequences and absolutely pure modules. And then, we give some new characterizations of $S$-coherent rings in terms of $s$-absolutely pure modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14142 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some new module-theoretic characterizations of $S$-coherent rings Zhang, Xiaolei Commutative Algebra Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$. In this paper, we first introduce and study the notions of $s$-pure exact sequences and $s$-absolutely pure modules which extend the classical notions of pure exact sequences and absolutely pure modules. And then, we give some new characterizations of $S$-coherent rings in terms of $s$-absolutely pure modules. |
| title | Some new module-theoretic characterizations of $S$-coherent rings |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2411.14142 |