Artinian local cohomology modules

چکیده مقاله

Let $R$ be a commutative Noetherian ring, $\fa$ 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 $\H^i_\fa(M)$ is finitely generated for all $i<t$ then
$\Hom_R(R/\fa, \H^t_\fa(M))$ is finitely generated. In this paper it
is shown that if $\H^i_\fa(M)$ is Artinian for all $i<t$ then
$\Hom_R(R/\fa, \H^t_\fa(M))$ need not be Artinian but it has a
finitely generated submodule $N$ such that
$\Hom_R(R/\fa,\H^t_\fa(M))/N$ is Artinian.