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arXiv · 2502.19288

Tensor Products of Flat Cotorsion Modules and Cotorsion Dimension

Yonggang Hu·Linyu Ma·Xintian Wang
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Abstract

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.

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Yonggang Hu, Linyu Ma, Xintian Wang. 2025-02-26. Tensor Products of Flat Cotorsion Modules and Cotorsion Dimension. https://arxiv.org/abs/2502.19288

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