**Problem**. let be a commuative ring and a finitely generated prime ideal of Suppose that Prove that

**Solution**. Let and suppose that So and thus for some Write this system of equations as where is the matrix of coefficients and Then multiplying from the left by gives us: and hence since But for some So and hence This proves that The other side of the inclusion is trivial.

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Hi Yaghoub. Please answer to the e-mails I sent you, recently.

According to Exercise 2.2 of the book {\bf Commutative ring

theory, by H. Matsumura}, we have:

If $M$ is a finitely generated $R$-module, then

$\sqrt{ann(M/IM)}=\sqrt{ann(M)+I},$ where $I$ is an ideal of $R.$

Your exercise is a particular case of the above result, where

$M=I=P.$

To prove Exercise 2.2, consider $a\in ann(M/IM)$ and define

$\varphi:M\longrightarrow M,\; \varphi(m)=am.$ Now use Theorem 2.1

of the same reference.