Possible Duplicate:
Annihilator of a simple module
Let me ask the same question as before because I still have trouble understanding the problem.
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 it seems known that the annihilator $I=Ann_{C}(S)$ of $S$ is of the form $I=\mathfrak{m}C$ for some maximal ideal $\mathfrak{m}$ of $R$. Could anyone provide me of a proof?