# Extension functors of local cohomology modules

Document Type : Research Paper

Authors

Abstract

Let $R$ be a commutative Noetherian ring with non-zero identity,
$fa$ an ideal of $R$, and $X$ an $R$--module. Here, for fixed
integers $s, t$ and a finite $fa$--torsion $R$--module $N$, we
first study the membership of $Ext^{s+t}_{R}(N, X)$ and
$Ext^{s}_{R}(N, H^{t}_{fa}(X))$ in the Serre subcategories of
the category of $R$--modules. Then, we present some conditions
which ensure the existence of an isomorphism between them.
Finally, we introduce the concept of the Serre cofiniteness as a
generalization of cofiniteness and study this property for
certain local cohomology modules.

Keywords

### History

• Receive Date: 07 October 2009
• Revise Date: 15 March 2012
• Accept Date: 30 January 2010