Artin-Rees theorem

Let $A$ be a Noetherian ring, $𝔞$ 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

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

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