A note on $S$-flat preenvelopes
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916362783293440 |
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| author | Zhang, Xiaolei |
| author_facet | Zhang, Xiaolei |
| contents | In this note, we investigate the notion of $S$-flat preenvelopes of modules. In particular, we give an example that a ring $R$ being coherent does not imply that every $R$-module have an $S$-flat preenvelope, giving a negative answer to the question proposed by Bennis and Bouziri \cite{BB24}. Besides, we also show that $R_S$ is a coherent ring also does not imply that $R$ is an $S$-coherent ring in general. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10523 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on $S$-flat preenvelopes Zhang, Xiaolei Commutative Algebra In this note, we investigate the notion of $S$-flat preenvelopes of modules. In particular, we give an example that a ring $R$ being coherent does not imply that every $R$-module have an $S$-flat preenvelope, giving a negative answer to the question proposed by Bennis and Bouziri \cite{BB24}. Besides, we also show that $R_S$ is a coherent ring also does not imply that $R$ is an $S$-coherent ring in general. |
| title | A note on $S$-flat preenvelopes |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2408.10523 |