Bulletin of the Korean Mathematical Society (대한수학회보)

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A NOTE ON 𝜙-PRÜFER ν-MULTIPLICATION RINGS

  • Zhang, Xiaolei (School of Mathematical Sciences Qufu Normal University and School of Mathematics and Statistics Shandong University of Technology)
  • Received : 2021.10.14
  • Accepted : 2022.02.10
  • Published : 2022.09.30
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Abstract

In this note, we show that a strongly 𝜙-ring R is a 𝜙-PvMR if and only if any 𝜙-torsion-free R-module is 𝜙-w-flat, if and only if any GV-torsion-free divisible R-module is nonnil-absolutely w-pure, if and only if any GV-torsion-free h-divisible R-module is nonnil-absolutely w-pure, if and only if any finitely generated nonnil ideal of R is w-projective.

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Acknowledgement

The author is very grateful to the reviewer for reading carefully the paper and pointing out errors in the proofs of Theorem 2.13 and Theorem 3.13 in the original version. The author was supported by the National Natural Science Foundation of China (No. 12061001).

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