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# Artin-Rees theorem

Let $A$ be a Noetherian ring, $\mathfrak{a}$ an ideal, $M$ a finitely generated module, and $N$ a submodule. Then there exists an integer $k\geq 1$ such that for all integers $n\geq 1$ we have

$\mathfrak{a}^{n}M\cap N=\mathfrak{a}^{{n-k}}(\mathfrak{a}^{k}M\cap N).$ |

Type of Math Object:

Theorem

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Reference

## Mathematics Subject Classification

13C99*no label found*

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