Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Weak u-S-flat Modules and Dimensions

  • Received : 2022.08.21
  • Accepted : 2022.11.28
  • Published : 2023.09.30
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Abstract

In this paper, we generalize the notions uniformly S-flat, briefly u-S-flat, modules and dimensions. We introduce and study the notions of weak u-S-flat modules. An R-module M is said to be weak u-S-flat if TorR1 (R/I, M) is u-S-torsion for any ideal I of R. This new class of modules will be used to characterize u-S-von Neumann regular rings. Hence, we introduce the weak u-S-flat dimensions of modules and rings. The relations between the introduced dimensions and other (classical) homological dimensions are discussed.

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References

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