Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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HOMOLOGY AND SERRE CLASS IN D(R)

  • Zhicheng, Wang (Department of Mathematics Northwest Normal University)
  • Received : 2021.09.22
  • Accepted : 2022.10.28
  • Published : 2023.01.31
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Abstract

Let 𝓢 be a Serre class in the category of modules and 𝖆 an ideal of a commutative Noetherian ring R. We study the containment of Tor modules, Koszul homology and local homology in 𝓢 from below. With these results at our disposal, by specializing the Serre class to be Noetherian or zero, a handful of conclusions on Noetherianness and vanishing of the foregoing homology theories are obtained. We also determine when TorR𝓼+t(R/𝖆, X) ≅ TorR𝓼(R/𝖆, H𝖆t(X)).

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References

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