Let $R$ be a commutative Noetherian ring, $I$ is a proper ideal of $R$ and $M$ is f.g. $R$-module. I want to find an example such that if $c:=\sup\{i\in \mathbb{N_0} \mid \textrm{Ext}_R^i(R/I,M)\neq 0\}$ and $c$ is finite then $c\gneqq \dim(R)$.
thanks for help