A homological characterization of Q0-Prüfer v-multiplication rings

Year 2022, , 228 - 240, 16.07.2022

Xiaolei Zhang

https://doi.org/10.24330/ieja.1077664

Abstract

Let $R$ be a commutative ring. An $R$-module $M$ is called a semi-regular $w$-flat module if $\Tor_1^R(R/I,M)$ is $\GV$-torsion for any finitely generated semi-regular ideal $I$. In this article, we show that the class of semi-regular $w$-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 $Q_0$-\PvMR s.

Keywords

Semi-regular $w$-flat module, $sr$-$w$-weak global dimension, $\WQ$-ring, $Q_0$-\PvMR

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