Cotorsion modules relative to a hereditary torsion theory

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, Prüfer $v$-multiplication domains, Dedekind domains, Krull domains, and DW-rings) are characterized in terms of these classes of modules.

arXiv comment28 pages