Artin-Rees lemma

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In mathematics, the Artin-Rees lemma (also known as the Artin-Rees theorem) is a result in the theory of rings and modules. It was proved in the 1950s in independent works by the mathematicians Emil Artin and David Rees; a special case was known to Oscar Zariski prior to their work. The result is used to prove the exactness property of completion(Atiyah & MacDonald 1969, pp. 107–109).

[edit] Statement of the result

Let I be an ideal in a Noetherian ring R; let M be a finitely generated R-module and let N a submodule of M. Then there exists an integer k ≥ 1 so that, for n ≥ k,

[edit] External links

• Artin-Rees Theorem on PlanetMath

[edit] References

This article needs additional citations for verification. Please help improve this article by adding reliable references. Unsourced material may be challenged and removed. (August 2007)

• Atiyah, Michael Francis & Macdonald, I.G. (1969), Introduction to Commutative Algebra, Westview Press, ISBN 978-0-201-40751-8