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Paper   IPM / M / 11810
School of Mathematics
  Title:   Artinianness of certain graded local cohomology modules
  Author(s):  A. Mafi (Joint with H. Saremi)
  Status:   Published
  Journal: Canad. Math. Bull.
  Vol.:  55
  Year:  2012
  Pages:   153-156
  Supported by:  IPM
e show that if R=⊕n ∈ \mathbbN0 Rn is a Noetherian homogeneous ring with local base ring (R0,\mathfrakm0), irrelevant ideal R+, and M a finitely generated graded R-module, then Hj\mathfrakm0R(HtR+(M)) is Artinian for j = 0, 1 where t = inf{i ∈ \mathbbN0: HiR+(M) is not finitely generated}. Also, we prove that if cd(R+,M) = 2, then for each i ∈ \mathbbN0, Hi\mathfrakm0R(H2R+(M)) is Artinian if and only if Hi+2\mathfrakm0R(H1R+(M)) is Artinian, where cd(R+,M) is the cohomological dimension of M with respect to R+. This improves some results of R. Sazeedeh.

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