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Paper   IPM / M / 8310
School of Mathematics
Title:   Associated primes of the local cohomology modules
Author(s):
 1 M. T. Dibaei 2 S. Yassemi
Status:   In Proceedings
Proceeding: Abelian groups, rings, modules, and homological algebras
Year:  2006
Pages:   51-58
Editor:  P. Goeters and O. M. G. Jenda
Supported by:  IPM
Abstract:
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 ExtsjR(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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