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Paper   IPM / M / 8718
School of Mathematics
  Title:   Finiteness of graded local cohomology modules
  Author(s):  R. Sazeedeh
  Status:   Published
  Journal: J. Pure Appl. Algebra
  Vol.:  212
  Year:  2008
  Pages:   275-280
  Supported by:  IPM
Let R = ⊕n ∈ \mathbbN0Rn be a Noetherian homogeneous ring with local base ring (R0, \frakm0) and irre1evant ideal R+, let M be a finitely generated graded R-module. In this paper we show that H1\frakm0R(H1R+(M)) is Artinian and Hi\frakm0R(H1R+(M)) is Artinian for each i in the case where R+ is principal. Moreover, for the case where ara(R+) = 2, we prove that, for each i ∈ \mathbbN0, Hi\frakm0R(H1R+(M)) is Artinian if and only if Hi+2\frakm0R(H1R+(M)) is Artinian. We also prove that Hd\frakm0R(HcR+(M)) is Artinian, where d = dim(R0) and c is the cohomological dimension of M with respect to R+. Finally we present some examples which show that H2\frakm0R(H1R+(M)) and H3\frakm0R(H1R+(M)) need not be Artinian.

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