On injective resolutions of local cohomology modules

Abstract

Let $K$ be a field of characteristic zero and let $R=K[X_1,\dots ,X_n]$. 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 $c=injdimM$. 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 $R$.