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| Paper IPM / M / 8716 |
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| Abstract: | |
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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)))∩{\frakp ∈ Spec(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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