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Some criteria for the Cohen-Macaulay property and local cohomology

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Abstract

Let a be an ideal of a commutative Noetherian ring R and M be a finitely generated R-module of dimension d. We characterize Cohen-Macaulay rings in term of a special homological dimension. Lastly, we prove that if R is a complete local ring, then the Matlis dual of top local cohomology module H d a (M) is a Cohen-Macaulay R-module provided that the R-module M satisfies some conditions.

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Authors and Affiliations

  1. Department of Mathematics, University of Kurdistan, P.O. Box: 416, Sanandaj, Iran

    Amir Mafi

  2. Institute for Studies in Theoretical Physics and Mathematics, P. O. Box 19395-5746, Tehran, Iran

    Amir Mafi

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  1. Amir Mafi
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Correspondence to Amir Mafi.

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This research is in part supported by a grant from IPM (No. 87130024)

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Mafi, A. Some criteria for the Cohen-Macaulay property and local cohomology. Acta. Math. Sin.-English Ser. 25, 917–922 (2009). https://doi.org/10.1007/s10114-009-7418-y

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  • DOI: https://doi.org/10.1007/s10114-009-7418-y

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