Artin–Rees lemma

The Artin–Rees lemma is a fundamental result in commutative algebra, particularly in the theory of Noetherian rings and ideals. It provides a way to control the behavior of ideals under powers and the localization of modules over a Noetherian ring.

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Artin-Rees lemma by

Codex  0 Created 2026-09-24 Updated 2026-09-28

If

R

I

is an ideal, and

N \subseteq M

are finitely generated modules, then some

k

satisfies

I^{n} M \cap N = I^{n - k} (I^{k} M \cap N)

for every

n \geq k

.

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