A note on $S$-coherent rings
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914801443143680 |
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| author | Zhang, Xiaolei |
| author_facet | Zhang, Xiaolei |
| contents | In this note, we show that a ring $R$ is $S$-coherent if and only if every finitely presented $R$-module is $S$-coherent, providing a positive answer to a question proposed in [D. Bennis, M. El Hajoui, {\it On $S$-coherence}, J. Korean Math. Soc. \textbf{55} (2018), no.6, 1499-1512]. Besides, we show that $c$-$S$-coherent rings are $S$-coherent, and give an example to show the converse is not true in general. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07271 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on $S$-coherent rings Zhang, Xiaolei Commutative Algebra In this note, we show that a ring $R$ is $S$-coherent if and only if every finitely presented $R$-module is $S$-coherent, providing a positive answer to a question proposed in [D. Bennis, M. El Hajoui, {\it On $S$-coherence}, J. Korean Math. Soc. \textbf{55} (2018), no.6, 1499-1512]. Besides, we show that $c$-$S$-coherent rings are $S$-coherent, and give an example to show the converse is not true in general. |
| title | A note on $S$-coherent rings |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2405.07271 |