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May 4th, 2009, 10:24 PM  #1 
Newbie Joined: Nov 2008 Posts: 2 Thanks: 0  Noetherian ring, finitely generated module
I need help with these two questions: 1. Let be a Noetherian ring, an ideal, and be modules. Suppose is reduced and are the minimal primes of . Prove that is a finitely generated module iff is a finitely generated module for each . 2. Now suppose is Artinian (need not be reduced). Prove that is Noetherian iff is Artinian. I know how to do #1 . But, I don't see how to do #1 . Also, for #2, I am stuck on both implications right now. Thanks in advance. 

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finitely, generated, module, noetherian, ring 
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