Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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(𝒱, 𝒲, 𝑦, 𝒳)-GORENSTEIN COMPLEXES

  • Yanjie Li (College of Mathematics and Statistics Northwest Normal University) ;
  • Renyu Zhao (College of Mathematics and Statistics Northwest Normal University, Gansu Provincial Research Center for Basic Disciplines of Mathematics and Statistics)
  • Received : 2023.08.31
  • Accepted : 2023.12.29
  • Published : 2024.05.01
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Abstract

Let 𝒱, 𝒲, 𝑦, 𝒳 be four classes of left R-modules. The notion of (𝒱, 𝒲, 𝑦, 𝒳)-Gorenstein R-complexes is introduced, and it is shown that under certain mild technical assumptions on 𝒱, 𝒲, 𝑦, 𝒳, an R-complex 𝑴 is (𝒱, 𝒲, 𝑦, 𝒳)-Gorenstein if and only if the module in each degree of 𝑴 is (𝒱, 𝒲, 𝑦, 𝒳)-Gorenstein and the total Hom complexs HomR(𝒀, 𝑴), HomR(𝑴, 𝑿) are exact for any ${\mathbf{Y}}\,{\in}\,{\tilde{\mathcal{Y}}}$ and any ${\mathbf{X}}\,{\in}\,{\tilde{\mathcal{X}}}$. Many known results are recovered, and some new cases are also naturally generated.

Keywords

Acknowledgement

The authors are grateful to the referee for the careful checking of this article and some helpful comments.

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