Cotorsion modules relative to a hereditary torsion theory

2026/07/30 by Lei Qiao
Mathematics · #math.AC #msc:13D07 #msc:13D30 #msc:13C13 #msc:13G05

paper · pdf

28 pages

arxiv created 2026/07/30 · arxiv updated 2026/07/31

Abstract

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.

Citations

• On Long-Term Problems in Multiplicative Ideal Theory and Factorization Theory
• S-flat cotorsion pair
• The small finitistic dimensions of commutative rings
• Two generalizations of projective modules and their applications
• On w-modules over strong mori domains

Related

• Torsion pairs over n-Hereditary rings
• On cotilting cotorsion and torsion pairs
• Cotorsion pairs and Tor-pairs over commutative noetherian rings
• On torsion-free modules and semi-hereditary rings
• A generalization of purely extending modules relative to a torsion theory