# Krull intersection theorem

Given a Noetherian ring $A$, an $A$-module $M$, and an ideal $I$ inside the radical of $A$, we have that $M$ is separated with respect to the $I$-adic topology.

Furthermore, if $A$ is also an integral domain and $J\subset A$ is a proper ideal, we have

 $\displaystyle\bigcap_{n>0}J^{n}=(0)$
Title Krull intersection theorem KrullIntersectionTheorem 2013-03-22 14:36:12 2013-03-22 14:36:12 mathcam (2727) mathcam (2727) 7 mathcam (2727) Theorem msc 13E05