##  [Artin–Rees Lemma](/artin-rees-lemma) 

  ##  [Artin–Rees Lemma](https://algebra.quantumdictionary.io/artin-rees-lemma-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A lemma describing the stable relationship between the powers of an ideal I acting on a finitely generated module M and a submodule N when the ring R is Noetherian: there exists k ≥ 0 such that for all n ≥ k, I^n M ∩ N = I^{n-k}(I^k M ∩ N), giving uniform control of intersections of filtrations.