# 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

 $\mathfrak{a}^{n}M\cap N=\mathfrak{a}^{n-k}(\mathfrak{a}^{k}M\cap N).$
Title Artin-Rees theorem ArtinReesTheorem 2013-03-22 12:41:03 2013-03-22 12:41:03 n3o (216) n3o (216) 7 n3o (216) Theorem msc 13C99