Artin-Rees lemma

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The Artin-Rees lemma is a theorem in commutative algebra, used to prove the exactness property of completion.

The statement of the most important special case of the theorem is as follows.

Let A be a commutative Noetherian ring, I an ideal of A, M a finitely-generated A-module, and N a submodule of M. Then there exists an integer k such that

for all n≥k.

This algebra-related article is a stub. You can help Wikipedia by expanding it.

Retrieved from "http://en.wikipedia.org../../../a/r/t/Artin-Rees_lemma_8cc3.html"

Categories: Algebra stubs | Commutative algebra | Lemmas

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• This page was last modified 21:51, 22 February 2007 by Wikipedia user NewEnglandYankee. Based on work by Wikipedia user(s) DavidCBryant, Oleg Alexandrov and Joeldl and Anonymous user(s) of Wikipedia.
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