Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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COHEN-MACAULAY DIMENSION FOR COMPLEXES

  • Received : 2023.06.26
  • Accepted : 2023.10.19
  • Published : 2024.04.30
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Abstract

In this paper, our focus lies in exploring the concept of Cohen-Macaulay dimension within the category of homologically finite complexes. We prove that over a local ring (R, 𝔪), any homologically finite complex X with a finite Cohen-Macaulay dimension possesses a finite CM-resolution. This means that there exists a bounded complex G of finitely generated R-modules, such that G is isomorphic to X and each nonzero Gi within the complex G has zero Cohen-Macaulay dimension.

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Acknowledgement

I would like to thank the referee for his/her detailed reading of this paper and thoughtful suggestions.

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