Let $R$ be a finitely generated commutative ring and $C$ an $R$-algebra ($C$ is not necessarily commutative). Assume that $C$ is a finitely generated $R$-module.
If $S$ is a simple $C$-module, then is the annihilator $I=Ann_{C}(S)$ of $S$ is of the form $I=\mathfrak{m}C$ for some maximal ideal $\mathfrak{m}$ of $R$?