The Krull Intersection theorem states that : For a finitely generated module $M$ over a Noetherian ring $R$ and any ideal $I$ of $R$, we have $I(\cap_{k=1}^{\infty}I^k M)=\cap_{k=1}^{\infty}I^k M$ .
The Artin-Rees lemma states that : For a finitely generated module $M$ over a Noetherian ring $R$ and for every ideal $I$ of $R$ , and submodule $N$ of $M$, there is an integer $k \ge 1$ such that $I^nM \cap N=I^{n-k} (I^kM \cap N), \forall n \ge k$ .
It is known that Krull intersection theorem can be derived from Artin-Rees lemma. My question is : Can the Artin-Rees lemma be derived from Krull intersection theorem ?