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| Paper IPM / M / 8613 |
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| Abstract: | |
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Let R be a commutative Noetherian ring, a an ideal of R and
M a finitely generated R-module. Let t be a non-negative
integer. It is known that if the local cohomology module
Hi\fraka(M) is finitely generated for all i < t, then
HomR(R/\fraka, Hi\fraka(M)) is finitely generated. In
this paper it is shown that if Hi\fraka(M) is Artinian
for all i < t, then HomR(R/\fraka, Hi\fraka(M))
need not be Artinian, but it has a finitely generated submodule
N such that HomR(R/\fraka, Hi\fraka(M)) is
Artinian.
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