SHMARQL

Artin–Rees lemma

<http://www.wikidata.org/entity/Q3229329>

lemma stating that, given an ideal I in a Noetherian commutative ring R and a submodule N of a a finitely generated R-module M, there exists a positive integer k such that, for every n≥k, IⁿM ∩ N = Iⁿ⁻ᵏ(IᵏM ∩ N)
rdfs:label
"Artin–Rees lemma"@en
skos:altLabel "Théorème d'Artin-Rees"@fr
"Théorème d'intersection de Krull"@fr
schema:description
"lemma stating that, given an ideal I in a Noetherian commutative ring R and a submodule N of a a finitely generated R-module M, there exists a positive integer k such that, for every n≥k, IⁿM ∩ N = Iⁿ⁻ᵏ(IᵏM ∩ N)"@en
schema:dateModified "2026-09-06T17:41:23+00:00"^^xsd:dateTime
schema:version 2541223854
wikibase:identifiers 2
wikibase:sitelinks 8
wikibase:statements 6
p:P138 wd:statement/Q3229329-bb47f071-4ba7-ff2e-3d28-bf22b945a860
wd:statement/Q3229329-cb491e6f-4d04-e3d2-f745-bca088bb235c
p:P31 wd:statement/Q3229329-f83b7d82-4d1a-f63b-5ff0-7f1afebe7ceb
p:P6104 wd:statement/Q3229329-A84D2B37-F431-4F51-825E-6E2B260086C0
p:P6366 wd:statement/Q3229329-A9B467AD-28A2-4BE2-B9F0-A01F836995F1
p:P646 wd:statement/Q3229329-638D5A99-D5EA-46E2-AE5F-2B8BC00362A5
p:direct-normalized/P6366 <https://makg.org/entity/2777141097>
wdt:P138 Emil Artin
David Rees
wdt:P31 theorem
wdt:P6104 WikiProject Mathematics
wdt:P6366 "2777141097"
wdt:P646 "/m/02pjrqz"
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