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Local Cohomology Modules and their Properties

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Ukrainian Mathematical Journal Aims and scope

Let (R,m) be a complete Noetherian local ring and let M be a generalized Cohen–Macaulay R-module of dimension d ≥ 2. We show that

$$ D\left({H}_m^d\left(D\left({H}_m^d\left({D}_m(M)\right)\right)\right)\right)\approx {D}_m(M), $$

where D = Hom(−,E) and Dm(−) is the ideal transform functor. In addition, by assuming that I is a proper ideal of a local ring R, we obtain some results on finiteness of the Bass numbers, cofiniteness, and cominimaxness of the local cohomology modules with respect to I.

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Authors and Affiliations

  1. University of Mohaghegh Ardabili, Ardabil, Iran

    J. Azami & M. Hasanzad

Authors
  1. J. Azami
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  2. M. Hasanzad
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Correspondence to J. Azami.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 2, pp. 268–274, February, 2021. Ukrainian DOI: 10.37863/umzh.v73i2.127.

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Azami, J., Hasanzad, M. Local Cohomology Modules and their Properties. Ukr Math J 73, 311–319 (2021). https://doi.org/10.1007/s11253-021-01924-z

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  • DOI: https://doi.org/10.1007/s11253-021-01924-z

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