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# Artin-Rees theorem

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

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

Type of Math Object:

Theorem

Major Section:

Reference

## Mathematics Subject Classification

13C99*no label found*

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new question: Prove that for any sets A, B, and C, An(BUC)=(AnB)U(AnC) by St_Louis

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new question: Prove that for any sets A, B, and C, An(BUC)=(AnB)U(AnC) by St_Louis

Apr 20

new image: information-theoretic-distributed-measurement-dds.png by rspuzio

new image: information-theoretic-distributed-measurement-4.2 by rspuzio

new image: information-theoretic-distributed-measurement-4.1 by rspuzio

new image: information-theoretic-distributed-measurement-3.2 by rspuzio

new image: information-theoretic-distributed-measurement-3.1 by rspuzio

new image: information-theoretic-distributed-measurement-2.1 by rspuzio

Apr 19

new collection: On the Information-Theoretic Structure of Distributed Measurements by rspuzio

Apr 15

new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia