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arXiv · 2607.28389

Cotorsion modules relative to a hereditary torsion theory

Lei Qiao
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Abstract

This paper investigates various classes of cotorsion modules relative to the hereditary torsion theory $\tau_w$ induced by the so-called $w$-operation. To achieve this, we first introduce the Tor and cotorsion pairs relative to $\tau_w$, which serve as our main tool. Additionally, we also introduce and study the strongly flat modules relative to $\tau_w$. As applications, several known rings (including perfect rings, almost perfect domains, Pr\"{u}fer $v$-multiplication domains, Dedekind domains, Krull domains, and DW-rings) are characterized in terms of these classes of modules.

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Lei Qiao. 2026-07-30. Cotorsion modules relative to a hereditary torsion theory. https://arxiv.org/abs/2607.28389

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