A homological characterization of $Q_0$-Prüfer $v$-multiplication rings

Abstract

Let R be a commutative ring. An R-module M is called a semi-regular w-flat module if Tor R 1 (R/I, M) is GV-torsion for any finitely generated semi-regular ideal I. In this article, we showed that the class of semiregular w-flat modules is a covering class. Moreover, we introduce the semi-regular w-flat dimensions of R-modules and the sr-w-weak global dimensions of the commutative ring R. Utilizing these notions, we give some homological characterizations of WQ-rings and Q 0 -PvMRs.