Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2022; 59(1): 213-226

Online first article January 3, 2022      Printed January 31, 2022

https://doi.org/10.4134/BKMS.b210242

Copyright © The Korean Mathematical Society.

A homological characterization of Pr\"ufer $v$-multiplication rings

Xiaolei Zhang

Shandong University of Technology

Abstract

Let $R$ be a ring and $M$ an $R$-module. Then $M$ is said to be regular $w$-flat provided that the natural homomorphism $I\otimes_R M \rightarrow R\otimes_R M$ is a $w$-monomorphism for any regular ideal $I$. We distinguish regular $w$-flat modules from regular flat modules and $w$-flat modules by idealization constructions. Then we give some characterizations of total quotient rings and Pr\"ufer\ $v$-multiplication rings (\PvMR s for short) utilizing the homological properties of regular $w$-flat modules.

Keywords: Regular $w$-flat module, regular $w$-weak global dimension, the total quotient ring, Pr\"ufer $v$-multiplication ring

MSC numbers: 13D05, 13A15

Supported by: The author was supported by the National Natural Science Foundation of China (No. 12061001).

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