“School of Mathematics”
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| Paper IPM / M / 8310 |
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| Abstract: | |||||
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In this article we will give some of the ideas we consider
important and point out the directions taken by some recent
research on the set of associated primes of the local cohomology
modules. In addition, we prove the following result.
Let R be a Noetherian ring and \fraka be an ideal of R.
Let M be an R-module and s be a non-negative integer. Then
the following hold:
(a) If Exts−jR(R/\fraka, Hj\fraka(M)) is
finitely generated for all j < s and if HomR(R/\fraka,Hs\fraka(M)) is a finitely generated R-module, then
ExtsR(R/\fraka, M) is a finitely generated R-module.
(b) If Exts+1−jR(R/\fraka, Hj\fraka(M)) is
finitely generated for all j < s and if ExtsR(R/\fraka,M)
is a finitely generated R-module, then HomR(R/\fraka,Hs\fraka(M)) is a finitely generated R-module.
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