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...

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

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

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...

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

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...

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...

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...

as Rees's theorem. The matrix-based semigroups used in this characterisation are called Rees matrix semigroups. Later in 1939, Welchman drafted Rees into...

still reasonably close to being additive, as a consequence of the Artin–Rees lemma. We denote by P I , M {\displaystyle P_{I,M}} the Hilbert-Samuel polynomial;...

d(D)>d(D/xD)\geq d(R/{\mathfrak {p}}_{1})} . (This essentially follows from the Artin–Rees lemma; see Hilbert–Samuel function for the statement and the proof.) In R...

ring satisfying the descending chain condition on ideals. 5.  The Artin-Rees lemma establishes a certain stability of filtration by an ideal. ASL Acronym...

1896) Known for Cayley–Dickson construction Dickson's conjecture Dickson's lemma Dickson invariant Dickson polynomial Modular invariant theory Awards Newcomb...

χ ( O X ) − 1 ) {\displaystyle (-1)^{r}(\chi ({\mathcal {O}}_{X})-1)} . Artin stack Another term for an algebraic stack. artinian 0-dimensional and Noetherian...

researcher, and short fiction writer Mary Rees (born 1953), British specialist in complex dynamical systems Mina Rees (1902–1997), first female President of...