In mathematics, the Artin–Rees lemma is a basic result about modules over a Noetherian ring, along with results such as the Hilbert basis theorem. It was...

reciprocity Artin–Rees lemma Artin representation Artin–Schreier theorem Artin–Schreier theory Artin's theorem on induced characters Artin–Zorn theorem...

theory) Zassenhaus lemma Gauss's lemma (polynomials) Schwartz–Zippel lemma Artin–Rees lemma Hensel's lemma (commutative rings) Nakayama lemma Noether's normalization...

finitely presented modules form an abelian category. Integral element Artin–Rees lemma Countably generated module Finite algebra For example, Matsumura uses...

when R is Noetherian and M finitely generated. This follows from the Artin-Rees lemma. When M is Hausdorff, M can be completed as a metric space; the resulting...

Hausdorff space. The theorem is a consequence of the Artin–Rees lemma together with Nakayama's lemma, and, as such, the "Noetherian" assumption is crucial...

Noetherian ring is defined in terms of ascending chains of ideals. The Artin–Rees lemma, on the other hand, gives some information about a descending chain...

Fitting lemma Schur's lemma Nakayama's lemma Krull–Schmidt theorem Steinitz exchange lemma Jordan–Hölder theorem Artin–Rees lemma Schanuel's lemma Morita...

compatible with F∗An(K), essentially parallel to the situation of the Artin–Rees lemma. The Hilbert polynomial is defined to be the numerical polynomial that...

ring” is used to invoke the Artin–Rees lemma and can be weakened; see Following SGA 1, Exposé IV, we first prove a few lemmas, which are interesting themselves...