Artin–Rees Lemma

A lemma describing the stable relationship between the powers of an ideal I acting on a finitely generated module M and a submodule N when the ring R is Noetherian: there exists k ≥ 0 such that for all n ≥ k, I^n M ∩ N = I^{n-k}(I^k M ∩ N), giving uniform control of intersections of filtrations.