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).

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