I need help with these two questions:

1. Let $\displaystyle R$ be a Noetherian ring, $\displaystyle I$ an ideal, and $\displaystyle N \subseteq M$ be $\displaystyle R$-modules. Suppose $\displaystyle R$ is reduced and $\displaystyle P_1, \ldots, P_n$ are the minimal primes of $\displaystyle R$. Prove that $\displaystyle M$ is a finitely generated $\displaystyle R$-module iff $\displaystyle \frac{M}{P_iM}$ is a finitely generated $\displaystyle \frac{R}{P_i}$-module for each $\displaystyle i=1, \ldots, n$.

2. Now suppose $\displaystyle R$ is Artinian (need not be reduced). Prove that $\displaystyle M$ is Noetherian iff $\displaystyle M$ is Artinian.

I know how to do #1 $\displaystyle (\Rightarrow)$. But, I don't see how to do #1 $\displaystyle (\Leftarrow)$. Also, for #2, I am stuck on both implications right now. Thanks in advance.