Artin-Rees lemma
= Artin-Rees lemma
{c}
{wiki=Artin–Rees_lemma}
If $R$ is Noetherian, $I$ is an ideal, and $N\subseteq M$ are finitely generated modules, then some $k$ satisfies
$$
I^nM\cap N=I^{n-k}(I^kM\cap N)
$$
for every $n\ge k$.
= Artin-Rees lemma
{c}
{wiki=Artin–Rees_lemma}
If $R$ is Noetherian, $I$ is an ideal, and $N\subseteq M$ are finitely generated modules, then some $k$ satisfies
$$
I^nM\cap N=I^{n-k}(I^kM\cap N)
$$
for every $n\ge k$.