Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A HOMOLOGICAL CHARACTERIZATION OF PRÜFER v-MULTIPLICATION RINGS

  • Zhang, Xiaolei (School of Mathematics and Statistics Shandong University of Technology)
  • Received : 2021.03.27
  • Accepted : 2021.10.14
  • Published : 2022.01.31
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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 ⊗R M → R ⊗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 Prüfer v-multiplication rings (PvMRs for short) utilizing the homological properties of regular w-flat modules.

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Acknowledgement

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

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