My Math Forum  

Go Back   My Math Forum > College Math Forum > Abstract Algebra

Abstract Algebra Abstract Algebra Math Forum

LinkBack Thread Tools Display Modes
May 4th, 2009, 10:24 PM   #1
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.
xianghu324 is offline  

  My Math Forum > College Math Forum > Abstract Algebra

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 03:30 AM
Prove S is not finitely generated. please help kennedy Linear Algebra 1 October 1st, 2009 03:59 PM
Noetherian, finitely generated R-module poincare4223 Abstract Algebra 0 April 29th, 2009 09:01 PM
Finitely Generated payman_pm Abstract Algebra 7 September 19th, 2007 04:21 AM
T-groups finitely generated sastra81 Abstract Algebra 0 January 3rd, 2007 06:54 AM

Copyright © 2019 My Math Forum. All rights reserved.