For $M$ any finitely generated $R$-module determine $E_R(M)$.

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Let $R$ be a principal ideal domain with quotient field $K$.

  1. For $p$ any prime element of $R$ and $P$ the prime ideal it generates, show that $$ E_R\left(R/P\right) \cong K/pR_p \cong K/R_p \cong R[p^{-1}]/R $$

I have already done this part.

  1. For $M$ any finitely generated $R$-module determine $E_R(M)$.

I assume that I am suppose to use part 1 to do part 2 but I can see how to do that?