Lemma di Artin-Rees

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 “Lemma di Artin-Rees” in Italian Wikipedia has 4 points for quality (as of July 1, 2025). The article contains 0 references and 4 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 “Lemma di Artin-Rees”, its content was written by 11 registered users of Italian Wikipedia and edited by 66 registered Wikipedia users in all languages.

The article is cited 1 times in Italian Wikipedia and cited 64 times in all languages.

The highest Authors Interest rank from 2001:

• Local (Italian): #12926 in March 2011
• Global: #168542 in March 2015

The highest popularity rank from 2008:

• Local (Italian): #517646 in June 2011
• 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.

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

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

The most popular language versions of the article "Lemma di Artin-Rees" in all the time

#	Language	Popularity award	Relative popularity
1	English (en) Artin–Rees lemma		68 009
2	French (fr) Lemme d'Artin-Rees		9 381
3	Japanese (ja) アルティン・リースの補題		8 333
4	German (de) Satz von Artin-Rees		4 342
5	Italian (it) Lemma di Artin-Rees		3 078
6	Persian (fa) قضیه آرتین–ریس		2 312
7	Portuguese (pt) Lema de Artin-Rees		457
8	Ukrainian (uk) Лема Артіна — Ріса		131

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

The most popular language versions of the article "Lemma di Artin-Rees" in June 2025

#	Language	Popularity award	Relative popularity
1	English (en) Artin–Rees lemma		447
2	Japanese (ja) アルティン・リースの補題		77
3	French (fr) Lemme d'Artin-Rees		51
4	German (de) Satz von Artin-Rees		28
5	Persian (fa) قضیه آرتین–ریس		14
6	Italian (it) Lemma di Artin-Rees		11
7	Portuguese (pt) Lema de Artin-Rees		6
8	Ukrainian (uk) Лема Артіна — Ріса		5

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

Language versions of the article "Lemma di Artin-Rees" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.

#	Language	AI award	Relative AI
1	English (en) Artin–Rees lemma		27
2	French (fr) Lemme d'Artin-Rees		12
3	Italian (it) Lemma di Artin-Rees		11
4	German (de) Satz von Artin-Rees		6
5	Japanese (ja) アルティン・リースの補題		5
6	Persian (fa) قضیه آرتین–ریس		2
7	Portuguese (pt) Lema de Artin-Rees		2
8	Ukrainian (uk) Лема Артіна — Ріса		1

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

Language versions of the article "Lemma di Artin-Rees" with the highest AI in June 2025

#	Language	AI award	Relative AI
1	German (de) Satz von Artin-Rees		0
2	English (en) Artin–Rees lemma		0
3	Persian (fa) قضیه آرتین–ریس		0
4	French (fr) Lemme d'Artin-Rees		0
5	Italian (it) Lemma di Artin-Rees		0
6	Japanese (ja) アルティン・リースの補題		0
7	Portuguese (pt) Lema de Artin-Rees		0
8	Ukrainian (uk) Лема Артіна — Ріса		0

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

Language versions of the article "Lemma di Artin-Rees" with the highest Citation Index (CI)

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

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#	Language	Value
de	German Satz von Artin-Rees
en	English Artin–Rees lemma
fa	Persian قضیه آرتین–ریس
fr	French Lemme d'Artin-Rees
it	Italian Lemma di Artin-Rees
ja	Japanese アルティン・リースの補題
pt	Portuguese Lema de Artin-Rees
uk	Ukrainian Лема Артіна — Ріса

Best Rank

Italian: #517646 06.2011

Global: #543643 01.2015

Best Rank

Italian: #12926 03.2011

Global: #168542 03.2015

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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