# 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

$\bigcap _{n>0}}{J}^{n}=(0)$ |

Title | Krull intersection theorem |
---|---|

Canonical name | KrullIntersectionTheorem |

Date of creation | 2013-03-22 14:36:12 |

Last modified on | 2013-03-22 14:36:12 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 7 |

Author | mathcam (2727) |

Entry type | Theorem |

Classification | msc 13E05 |