# Artin-Rees theorem

Let $A$ be a Noetherian ring^{}, $\U0001d51e$ an ideal, $M$ a finitely generated module, and $N$ a submodule^{}. Then there exists an integer $k\ge 1$ such that for all integers $n\ge 1$ we have

$${\U0001d51e}^{n}M\cap N={\U0001d51e}^{n-k}({\U0001d51e}^{k}M\cap N).$$ |

Title | Artin-Rees theorem |
---|---|

Canonical name | ArtinReesTheorem |

Date of creation | 2013-03-22 12:41:03 |

Last modified on | 2013-03-22 12:41:03 |

Owner | n3o (216) |

Last modified by | n3o (216) |

Numerical id | 7 |

Author | n3o (216) |

Entry type | Theorem |

Classification | msc 13C99 |