Tensor Products of Flat Cotorsion Modules and Cotorsion Dimension
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917937435115520 |
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| author | Hu, Yonggang Ma, Linyu Wang, Xintian |
| author_facet | Hu, Yonggang Ma, Linyu Wang, Xintian |
| contents | This paper studies the tensor product of flat cotorsion modules. Let~$R$~and $S$ be~$k$-algebras. We prove that both~$R$-module\ $M$ and~$S$-module\ $N$ are flat cotorsion modules if and only if~$M\otimes_{k} N$ is a flat cotorsion~$R\otimes_{k} S $-module. Based on this conclusion, we provide a lower bound for the global cotorsion dimension of the tensor product algebra~$R\otimes_{k}S $ under appropriate conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19288 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tensor Products of Flat Cotorsion Modules and Cotorsion Dimension Hu, Yonggang Ma, Linyu Wang, Xintian Rings and Algebras This paper studies the tensor product of flat cotorsion modules. Let~$R$~and $S$ be~$k$-algebras. We prove that both~$R$-module\ $M$ and~$S$-module\ $N$ are flat cotorsion modules if and only if~$M\otimes_{k} N$ is a flat cotorsion~$R\otimes_{k} S $-module. Based on this conclusion, we provide a lower bound for the global cotorsion dimension of the tensor product algebra~$R\otimes_{k}S $ under appropriate conditions. |
| title | Tensor Products of Flat Cotorsion Modules and Cotorsion Dimension |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2502.19288 |