A question in noetherian ring!
- From: Cooper <cooper0040@xxxxxxxxx>
- Date: Sun, 29 Jul 2007 09:33:04 -0700
Hi!
The question I want to ask is following;
Let M be a finitely generated R-module, where R is noetherian. Suppose
I is an ideal of R such that for each element a in I, there exists a
nonzero element x in M s.t. xa=0. Show that xI=0 for some nonzero
element x in M.
The product of all x_i's which satisfy x_i * a_i=0 where a_i's are
finite generator of I would fail because R is not domain. How to use
the condition M is finitely generated?
.
- Follow-Ups:
- Re: A question in noetherian ring!
- From: galathaea
- Re: A question in noetherian ring!
- From: quasi
- Re: A question in noetherian ring!
- From: rusty
- Re: A question in noetherian ring!
- Prev by Date: Re: JSH: Update on DMESE and how they lie
- Next by Date: Re: If you need a solution manual or if you have one contact me (over 200 and counting)
- Previous by thread: Von Neumann was right - At least about Poker
- Next by thread: Re: A question in noetherian ring!
- Index(es):
Relevant Pages
|
