# Artin–Rees lemma

> lemma stating that, given an ideal I in a Noetherian commutative ring R and a submodule N of a a finitely generated R-module M, there exists a positive integer k such that, for every n≥k, IⁿM ∩ N = Iⁿ⁻ᵏ(IᵏM ∩ N)

**Wikidata**: [Q3229329](https://www.wikidata.org/wiki/Q3229329)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Artin–Rees_lemma)  
**Source**: https://4ort.xyz/entity/artin-rees-lemma


## References

1. Freebase Data Dumps. 2013