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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.06458 |
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| _version_ | 1866918119417577472 |
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| author | Asadollahi, Javad Hafezi, Rasool Sadeghi, Somayeh |
| author_facet | Asadollahi, Javad Hafezi, Rasool Sadeghi, Somayeh |
| contents | In this paper, we investigate a non-commutative version of strongly flat modules, which is based on the concept of universal localization introduced by Cohn. We consider a set $σ$ consisting of maps of finitely generated projective $R$-modules, where $R$ is not necessarily a commutative ring. Let $R_σ$ denote the universal localization of $R$ with respect to $σ$. The class of $σ$-strongly flat modules is defined as the left class in the cotorsion pair generated by $R_σ$. We examine the homotopy category of $σ$-strongly flat modules and demonstrate that the thick subcategory $\mathscr{S}_σ$, consisting of acyclic complexes, wherein all syzygies are $σ$-strongly flat, forms a precovering class within this homotopy category. This implies that the quotient map from $\mathbb{K}({σ\mbox{-}\mathcal{SF}})$ to $\mathbb{K}({σ\mbox{-}\mathcal{SF}})/\mathscr{S}_σ$ always has a fully faithful right adjoint. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06458 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strongly flat modules via universal localization Asadollahi, Javad Hafezi, Rasool Sadeghi, Somayeh Representation Theory 18E35, 55P60, 16S85, 16E30 In this paper, we investigate a non-commutative version of strongly flat modules, which is based on the concept of universal localization introduced by Cohn. We consider a set $σ$ consisting of maps of finitely generated projective $R$-modules, where $R$ is not necessarily a commutative ring. Let $R_σ$ denote the universal localization of $R$ with respect to $σ$. The class of $σ$-strongly flat modules is defined as the left class in the cotorsion pair generated by $R_σ$. We examine the homotopy category of $σ$-strongly flat modules and demonstrate that the thick subcategory $\mathscr{S}_σ$, consisting of acyclic complexes, wherein all syzygies are $σ$-strongly flat, forms a precovering class within this homotopy category. This implies that the quotient map from $\mathbb{K}({σ\mbox{-}\mathcal{SF}})$ to $\mathbb{K}({σ\mbox{-}\mathcal{SF}})/\mathscr{S}_σ$ always has a fully faithful right adjoint. |
| title | Strongly flat modules via universal localization |
| topic | Representation Theory 18E35, 55P60, 16S85, 16E30 |
| url | https://arxiv.org/abs/2508.06458 |