Bulletin of the Korean Mathematical Society (대한수학회보)

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ON ARTINIANNESS OF GENERAL LOCAL COHOMOLOGY MODULES

  • Tri, Nguyen Minh (Department of Natural Science Education Dong Nai University)
  • Received : 2020.05.26
  • Accepted : 2021.03.08
  • Published : 2021.05.31
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Abstract

In this paper, we show some results on the artinianness of local cohomology modules with respect to a system of ideals. If M is a 𝚽-minimax ZD-module, then Hdim M𝚽(M)/𝖆Hdim M𝚽(M) is artinian for all 𝖆 ∈ 𝚽. Moreover, if M is a 𝚽-minimax ZD-module, t is a non-negative integer and Hi𝚽(M) is minimax for all i > t, then Hi𝚽(M) is artinian for all i > t.

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Acknowledgement

The author is deeply grateful to the referee for careful reading of the manuscript and for the helpful suggestions.

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