关于遗传挠理论的余挠模
Cotorsion modules relative to a hereditary torsion theory
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中文总结 AI 辅助
本文针对遗传挠理论τ_w，引入Tor对、余挠对及强平坦模，以此刻画完全环等多种已知环类。
中文摘要 AI 辅助
本文研究由所谓的w-运算诱导的遗传挠理论τ_w下的各类余挠模。为实现此目标，我们首先引入作为主要工具的、相对于τ_w的Tor对与余挠对，同时还引入并研究了相对于τ_w的强平坦模。作为应用，利用这些模类刻画了若干已知环，包括完全环、几乎完全整环、Prüfer v-乘法整环、戴德金整环、克鲁尔整环与DW-环。
英文摘要
This paper investigates various classes of cotorsion modules relative to the hereditary torsion theory $τ_w$ induced by the so-called $w$-operation. To achieve this, we first introduce the Tor and cotorsion pairs relative to $τ_w$, which serve as our main tool. Additionally, we also introduce and study the strongly flat modules relative to $τ_w$. As applications, several known rings (including perfect rings, almost perfect domains, Prüfer $v$-multiplication domains, Dedekind domains, Krull domains, and DW-rings) are characterized in terms of these classes of modules.
