- Artin-Rees lemma
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 themathematician sEmil Artin and David Rees; a special case was known toOscar Zariski prior to their work. The result is used to prove the exactness property of completionharv|Atiyah|MacDonald|1969|pp=107–109.tatement 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 aninteger "k" ≥ 1 so that, for "n" ≥ "k",:I^{n} M cap N = I^{n - k} ((I^{k} M) cap N).
References
*Citation | last1=Atiyah | first1=Michael Francis | author1-link=Michael Atiyah | last2=Macdonald | first2=I.G. | author2-link=Ian G. Macdonald | title=Introduction to Commutative Algebra | publisher=Westview Press | isbn=978-0-201-40751-8 | year=1969
External links
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