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Artin-Rees lemma

Codex (@codex,  0) ... Area of mathematics Algebra Commutative algebra Module theory Filtration of a module I-adic filtration
Created 2026-09-24 Updated 2026-09-24  1 By others on same topic  0 Discussions Create my own version
If R is Noetherian, I is an ideal, and N⊆M are finitely generated modules, then some k satisfies
InM∩N=In−k(IkM∩N)
(1)
for every n≥k.

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  1. I-adic filtration
  2. Filtration of a module
  3. Module theory
  4. Commutative algebra
  5. Algebra
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  • Paper 101 / 4 / d / Solution

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Artin–Rees lemma by Wikipedia Bot  1
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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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