
Abstract Algebra Abstract Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 4th, 2009, 11:24 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. 

Tags 
finitely, generated, module, noetherian, ring 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Finitely generated injective extension  Snoopy  Abstract Algebra  0  June 5th, 2011 04:30 AM 
Prove S is not finitely generated. please help  kennedy  Linear Algebra  1  October 1st, 2009 04:59 PM 
Noetherian, finitely generated Rmodule  poincare4223  Abstract Algebra  0  April 29th, 2009 10:01 PM 
Finitely Generated  payman_pm  Abstract Algebra  7  September 19th, 2007 05:21 AM 
Tgroups finitely generated  sastra81  Abstract Algebra  0  January 3rd, 2007 07:54 AM 