On injective resolutions of local cohomology modules

Abstract

Let $R=K[X_{1},\ldots,X_{n}]$ where $K$ is a field of characteristic zero. Let $I$ be an ideal in $R$ and let $M=H^{i}_{I}(R)$ be the $i$th-local cohomology module of $R$ with respect to $I$. Let $c=\operatorname{injdim} M$. We prove that if $P$ is a prime ideal in $R$ with Bass number $\mu_{c}(P,M)>0$ then $P$ is a maximal ideal in $R$.