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...
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reciprocity Artin–Rees lemma Artin representation Artin–Schreier theorem Artin–Schreier theory Artin's theorem on induced characters Artin–Zorn theorem...
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theory) Zassenhaus lemma Gauss's lemma (polynomials) Schwartz–Zippel lemma Artin–Rees lemma Hensel's lemma (commutative rings) Nakayama lemma Noether's normalization...
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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...
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Fitting lemma Schur's lemma Nakayama's lemma Krull–Schmidt theorem Steinitz exchange lemma Jordan–Hölder theorem Artin–Rees lemma Schanuel's lemma Morita...
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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...
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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...
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as Rees's theorem. The matrix-based semigroups used in this characterisation are called Rees matrix semigroups. Later in 1939, Welchman drafted Rees into...
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finitely presented modules form an abelian category. Integral element Artin–Rees lemma Countably generated module Finite algebra Coherent sheaf, a generalization...
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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...
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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;...
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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...
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ring satisfying the descending chain condition on ideals. 5. The Artin-Rees lemma establishes a certain stability of filtration by an ideal. ASL Acronym...
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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...
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1896) Known for Cayley–Dickson construction Dickson's conjecture Dickson's lemma Dickson invariant Dickson polynomial Modular invariant theory Awards Newcomb...
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researcher, and short fiction writer Mary Rees (born 1953), British specialist in complex dynamical systems Mina Rees (1902–1997), first female President of...
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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...
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