Re: A question in noetherian ring!

On Sun, 29 Jul 2007 09:33:04 -0700, Cooper <cooper0040@xxxxxxxxx>
wrote:

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.

Initially, I was almost sure the above claim was false, but after
several failed attempts to produce a counterexample, I'm no longer so
certain. Perhaps it's true, but I remain skeptical.

Was this an exercise from a text? If so, which?

quasi
.

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