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IPM
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“School of Mathematics”

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Paper   IPM / M / 8716
School of Mathematics
  Title:   On the finiteness results of the generalized local cohomology modules
  Author(s):  A. Mafi
  Status:   Published
  Journal: Algebra Colloq.
  Vol.:  16
  Year:  2009
  Pages:   325-332
  Supported by:  IPM
  Abstract:
Let \fraka be an ideal of a commutative Noetherian local ring R, and let M and N be two finitely generated R-modules. Let t be a positive integer. It is shown that if the support of the generalized local cohomology module Hi\fraka(M, N) is finite for all i < t, then the set of associated prime ideals of the generalized local cohomology module Ht\fraka(M,N) is finite. Also, if the support of the local co homology module Hi\fraka(N) is finite for all i < t, then the set (∪i ∈ \mathbbNAssR(ExttR(M/\frakaiM, N)))∩{\frakpSpec(R): dim R/ \frakp > 1} is finite. Moreover, we prove that gdepth (\fraka + Ann(M), N) is the least integer t such that the support of the generalized local co homology module Ht\fraka(M, N) is an infinite set.

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