Satz von Artin-Rees

de

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Satz von Artin-Rees

Quality:

Artin–Rees lemma - 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). Article “Satz von Artin-Rees” in German Wikipedia has 11.8 points for quality (as of July 1, 2025). The article contains 1 references and 3 sections.

This article has the best quality in Portuguese Wikipedia. However, the most popular language version of this article is English.

Since the creation of article “Satz von Artin-Rees”, its content was written by 6 registered users of German Wikipedia and edited by 66 registered Wikipedia users in all languages.

The article is cited 6 times in German Wikipedia and cited 64 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (German): #16321 in June 2013
  • Global: #168542 in March 2015

The highest popularity rank from 2008:

  • Local (German): #733732 in June 2013
  • Global: #543643 in January 2015

There are 8 language versions for this article in the WikiRank database (of the considered 55 Wikipedia language editions).

The quality and popularity assessment was based on Wikipédia dumps from July 1, 2025 (including revision history and pageviews for previous years).

The table below shows the language versions of the article with the highest quality.

Languages with the highest quality

#LanguageQuality gradeQuality score
1Portuguese (pt)
Lema de Artin-Rees
21.4821
2English (en)
Artin–Rees lemma
17.8309
3German (de)
Satz von Artin-Rees
11.8291
4Japanese (ja)
アルティン・リースの補題
7.8128
5Ukrainian (uk)
Лема Артіна — Ріса
7.5523
6French (fr)
Lemme d'Artin-Rees
5.5971
7Italian (it)
Lemma di Artin-Rees
4.025
8Persian (fa)
قضیه آرتین–ریس
3.1054
More...

The following table shows the most popular language versions of the article.

Most popular in all the time

The most popular language versions of the article "Satz von Artin-Rees" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Artin–Rees lemma
68 009
2French (fr)
Lemme d'Artin-Rees
9 381
3Japanese (ja)
アルティン・リースの補題
8 333
4German (de)
Satz von Artin-Rees
4 342
5Italian (it)
Lemma di Artin-Rees
3 078
6Persian (fa)
قضیه آرتین–ریس
2 312
7Portuguese (pt)
Lema de Artin-Rees
457
8Ukrainian (uk)
Лема Артіна — Ріса
131
More...

The following table shows the language versions of the article with the highest popularity in the last month.

Most popular in June 2025

The most popular language versions of the article "Satz von Artin-Rees" in June 2025
#LanguagePopularity awardRelative popularity
1English (en)
Artin–Rees lemma
447
2Japanese (ja)
アルティン・リースの補題
77
3French (fr)
Lemme d'Artin-Rees
51
4German (de)
Satz von Artin-Rees
28
5Persian (fa)
قضیه آرتین–ریس
14
6Italian (it)
Lemma di Artin-Rees
11
7Portuguese (pt)
Lema de Artin-Rees
6
8Ukrainian (uk)
Лема Артіна — Ріса
5
More...

The following table shows the language versions of the article with the highest Authors’ Interest.

The highest AI

Language versions of the article "Satz von Artin-Rees" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Artin–Rees lemma
27
2French (fr)
Lemme d'Artin-Rees
12
3Italian (it)
Lemma di Artin-Rees
11
4German (de)
Satz von Artin-Rees
6
5Japanese (ja)
アルティン・リースの補題
5
6Persian (fa)
قضیه آرتین–ریس
2
7Portuguese (pt)
Lema de Artin-Rees
2
8Ukrainian (uk)
Лема Артіна — Ріса
1
More...

The following table shows the language versions of the article with the highest Authors’ Interest in the last month.

The highest AI in June 2025

Language versions of the article "Satz von Artin-Rees" with the highest AI in June 2025
#LanguageAI awardRelative AI
1German (de)
Satz von Artin-Rees
0
2English (en)
Artin–Rees lemma
0
3Persian (fa)
قضیه آرتین–ریس
0
4French (fr)
Lemme d'Artin-Rees
0
5Italian (it)
Lemma di Artin-Rees
0
6Japanese (ja)
アルティン・リースの補題
0
7Portuguese (pt)
Lema de Artin-Rees
0
8Ukrainian (uk)
Лема Артіна — Ріса
0
More...

The following table shows the language versions of the article with the highest number of citations.

The highest CI

Language versions of the article "Satz von Artin-Rees" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1English (en)
Artin–Rees lemma
20
2Japanese (ja)
アルティン・リースの補題
16
3French (fr)
Lemme d'Artin-Rees
12
4German (de)
Satz von Artin-Rees
6
5Persian (fa)
قضیه آرتین–ریس
5
6Portuguese (pt)
Lema de Artin-Rees
2
7Ukrainian (uk)
Лема Артіна — Ріса
2
8Italian (it)
Lemma di Artin-Rees
1
More...

Scores

Estimated value for Wikipedia:
German:
Global:
Popularity in June 2025:
German:
Global:
Popularity in all years:
German:
Global:
Authors in June 2025:
German:
Global:
Registered authors in all years:
German:
Global:
Citations:
German:
Global:

Quality measures

Interwikis

#LanguageValue
deGerman
Satz von Artin-Rees
enEnglish
Artin–Rees lemma
faPersian
قضیه آرتین–ریس
frFrench
Lemme d'Artin-Rees
itItalian
Lemma di Artin-Rees
jaJapanese
アルティン・リースの補題
ptPortuguese
Lema de Artin-Rees
ukUkrainian
Лема Артіна — Ріса

Popularity rank trends

Best Rank German:
#733732
06.2013
Global:
#543643
01.2015

AI rank trends

Best Rank German:
#16321
06.2013
Global:
#168542
03.2015

Languages comparison

Important global interconnections (July 2024 – June 2025)

Wikipedia readers most often find their way to information on Artin–Rees lemma from Wikipedia articles about I-adic topology, Local ring, Noetherian ring, Finitely generated module and D-module. Whereas reading the article about Artin–Rees lemma people most often go to Wikipedia articles on Local ring, David Rees, Krulls intersection theorem, Nakayama lemma and ℓ-adic sheaf.

Cumulative results of quality and popularity of the Wikipedia article

List of Wikipedia articles in different languages (starting with the most popular):

News from 15 February 2026

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In German Wikipedia the most popular articles on that day were: Jeffrey Epstein, Cordelia Wege, Polizeiruf 110: Der Wanderer zieht von dannen, Lawrence von Arabien (Film), Medaillenspiegel der Olympischen Winterspiele 2026, Peter Kurth (Schauspieler), Die Tribute von Panem – The Ballad of Songbirds and Snakes, Olympische Winterspiele 2026/Eishockey (Herren), Olympische Winterspiele 2026, Federica Brignone.

About WikiRank

The WikiRank project is intended for automatic relative evaluation of the articles in the various language versions of Wikipedia. At the moment the service allows to compare over 44 million Wikipedia articles in 55 languages. Quality scores of articles are based on Wikipedia dumps from July, 2025. When calculating current popularity and AI of articles data from June 2025 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2025... More information