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I have a question about this statement:

Let $M$ be an $R$-module of finite length and let $\mbox{Ann}(M)\subset P_1,...,P_k$ be maximal ideals. If $n\in\mathbb{Z}_+$ is such that $P_1^n\cdots P_k^n\subset\mbox{Ann}(M)$, then the sequences $0\rightarrow P_i^nM \rightarrow M \rightarrow M_{P_i} \rightarrow 0$ are exact and $M/P_iM \cong M_{P_i}$.

I wonder what the maps are in these sequences. Especially what is the homomorphism $M \rightarrow M_{P_i}$? I especially wonder because I can not find such a surjective homomorphism.

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    Welcome to math.stackexchange! To get better answers, I would suggest editing your question to make it clearer what is given and what you understand and don't understand. For example, you use $P_i$ and $p_i$, is there any difference? Are you talking about localization? Then use $M_{p_i}$ Are you asking what are the maps in the sequence? etc.2012-12-03
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    because I can not log in to my account from the computer in my school for some reason! I am very sorry about that! And also, I wanted to email you, but didn't find any link on your page for doing that. I would be very thankful for your help though!2012-12-03

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