Corollary 1 (the Artin-Rees Lemma)

Tag 04G1, permanent. Cite it as [Bourbaki, Tag 04G1].

Commutative Algebra, chapter III, § 3. m-adic topologies on Noetherian rings

Let A be a commutative Noetherian ring, m an ideal of A, E a finitely generated A-module and F a submodule of E. The filtration induced on F by the m-adic filtration on E is m-good.

In other words, there exists an integer $n_0$ such that

m((m^n E) \cap F) = (m^{n+1} E) \cap F

for all $n \geq n_0$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Corollary 2, § 3
Corollary 3, § 3

Cites

Nothing.