IPM

“ Schools ”

“ Centers and Units ”

“ Research Groups ”

“ Useful Links ”

“ E-Services ”

“School of Mathematics”

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 Ext^s−j_R(R/\fraka, H^j_\fraka(M)) is finitely generated for all j < s and if Hom_R(R/\fraka,H^s_\fraka(M)) is a finitely generated R-module, then Ext^s_R(R/\fraka, M) is a finitely generated R-module.

(b) If Ext^s+1−j_R(R/\fraka, H^j_\fraka(M)) is finitely generated for all j < s and if Ext^s_R(R/\fraka,M) is a finitely generated R-module, then Hom_R(R/\fraka,H^s_\fraka(M)) is a finitely generated R-module.

Download TeX format