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April 29th, 2009, 09:01 PM  #1 
Newbie Joined: Dec 2008 Posts: 10 Thanks: 0  Noetherian, finitely generated Rmodule
I need help proving the following: 1. Let be a Noetherian ring, an ideal, and be modules. Let be a finitely generated module. Prove that is a finitely generated module. 2. Let be a Noetherian ring, an ideal of R. Prove that is a finitely generated module iff is a finitely generated module. The first problem seems to be straightforward. Can I just take the generators and multiply them by to show this is finitely generated? Thanks for any suggestions with this one. As for the second one, I am not seeing how to use the first part in this problem. I am guessing that I just let for one direction; but the other direction is confusing me. 

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finitely, generated, noetherian, rmodule 
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