Some remarks on almost projective envelopes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866910470572605440 |
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| author | Zhang, Xiaolei Qi, Wei Zhou, Dechuan |
| author_facet | Zhang, Xiaolei Qi, Wei Zhou, Dechuan |
| contents | Let $R$ be a commutative ring. An $R$-module $M$ is said to be almost projective if ${\rm Ext}^1_R(M, N) = 0$ for any $R_{\mathfrak{m}}$-module $N$ and any maximal ideal $\mathfrak{m}$ of $R$. In this paper, we investigate rings $R$ over which every $R$-module has an almost projective envelope. We also characterize rings $R$ over which every $R$-module has an almost projective envelope with some special properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02005 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some remarks on almost projective envelopes Zhang, Xiaolei Qi, Wei Zhou, Dechuan Commutative Algebra Let $R$ be a commutative ring. An $R$-module $M$ is said to be almost projective if ${\rm Ext}^1_R(M, N) = 0$ for any $R_{\mathfrak{m}}$-module $N$ and any maximal ideal $\mathfrak{m}$ of $R$. In this paper, we investigate rings $R$ over which every $R$-module has an almost projective envelope. We also characterize rings $R$ over which every $R$-module has an almost projective envelope with some special properties. |
| title | Some remarks on almost projective envelopes |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2406.02005 |