Structure theorem for finitely generated modules over a principal ideal domain

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Structure theorem for finitely generated modules over a principal ideal domain

Quality:

Structure theorem for finitely generated modules over a principal ideal domain - result in abstract algebra. Article "Structure theorem for finitely generated modules over a principal ideal domain" in English Wikipedia has 23.4 points for quality (as of July 1, 2025). The article contains 0 references and 12 sections.

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

Since the creation of article "Structure theorem for finitely generated modules over a principal ideal domain", its content was written by 57 registered users of English Wikipedia and edited by 116 registered Wikipedia users in all languages.

The article is cited 39 times in English Wikipedia and cited 202 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (English): #70585 in May 2009
  • Global: #112974 in July 2013

The highest popularity rank from 2008:

  • Local (English): #263216 in January 2015
  • Global: #418096 in January 2015

There are 7 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
1French (fr)
Théorème des facteurs invariants
34.2161
2Catalan (ca)
Teorema d'estructura dels mòduls finitament generats sobre un domini d'ideals principals
25.0953
3English (en)
Structure theorem for finitely generated modules over a principal ideal domain
23.3522
4Japanese (ja)
主イデアル整域上の有限生成加群の構造定理
10.6137
5Russian (ru)
Структурная теорема для конечнопорождённых модулей над областями главных идеалов
8.8699
6Ukrainian (uk)
Структурна теорема для скінченнопороджених модулів над областями головних ідеалів
8.3721
7Vietnamese (vi)
Định lý cấu trúc cho các mô đun hữu hạn sinh trên một vành chính
4.7366
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 "Structure theorem for finitely generated modules over a principal ideal domain" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Structure theorem for finitely generated modules over a principal ideal domain
271 974
2French (fr)
Théorème des facteurs invariants
68 100
3Japanese (ja)
主イデアル整域上の有限生成加群の構造定理
16 255
4Russian (ru)
Структурная теорема для конечнопорождённых модулей над областями главных идеалов
15 013
5Catalan (ca)
Teorema d'estructura dels mòduls finitament generats sobre un domini d'ideals principals
1 035
6Vietnamese (vi)
Định lý cấu trúc cho các mô đun hữu hạn sinh trên một vành chính
411
7Ukrainian (uk)
Структурна теорема для скінченнопороджених модулів над областями головних ідеалів
166
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 "Structure theorem for finitely generated modules over a principal ideal domain" in June 2025
#LanguagePopularity awardRelative popularity
1English (en)
Structure theorem for finitely generated modules over a principal ideal domain
1 520
2French (fr)
Théorème des facteurs invariants
323
3Japanese (ja)
主イデアル整域上の有限生成加群の構造定理
249
4Russian (ru)
Структурная теорема для конечнопорождённых модулей над областями главных идеалов
123
5Catalan (ca)
Teorema d'estructura dels mòduls finitament generats sobre un domini d'ideals principals
9
6Vietnamese (vi)
Định lý cấu trúc cho các mô đun hữu hạn sinh trên một vành chính
7
7Ukrainian (uk)
Структурна теорема для скінченнопороджених модулів над областями головних ідеалів
3
More...

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

The highest AI

Language versions of the article "Structure theorem for finitely generated modules over a principal ideal domain" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Structure theorem for finitely generated modules over a principal ideal domain
57
2French (fr)
Théorème des facteurs invariants
40
3Catalan (ca)
Teorema d'estructura dels mòduls finitament generats sobre un domini d'ideals principals
6
4Russian (ru)
Структурная теорема для конечнопорождённых модулей над областями главных идеалов
6
5Japanese (ja)
主イデアル整域上の有限生成加群の構造定理
3
6Ukrainian (uk)
Структурна теорема для скінченнопороджених модулів над областями головних ідеалів
2
7Vietnamese (vi)
Định lý cấu trúc cho các mô đun hữu hạn sinh trên một vành chính
2
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 "Structure theorem for finitely generated modules over a principal ideal domain" with the highest AI in June 2025
#LanguageAI awardRelative AI
1Catalan (ca)
Teorema d'estructura dels mòduls finitament generats sobre un domini d'ideals principals
0
2English (en)
Structure theorem for finitely generated modules over a principal ideal domain
0
3French (fr)
Théorème des facteurs invariants
0
4Japanese (ja)
主イデアル整域上の有限生成加群の構造定理
0
5Russian (ru)
Структурная теорема для конечнопорождённых модулей над областями главных идеалов
0
6Ukrainian (uk)
Структурна теорема для скінченнопороджених модулів над областями головних ідеалів
0
7Vietnamese (vi)
Định lý cấu trúc cho các mô đun hữu hạn sinh trên một vành chính
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 "Structure theorem for finitely generated modules over a principal ideal domain" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1French (fr)
Théorème des facteurs invariants
108
2English (en)
Structure theorem for finitely generated modules over a principal ideal domain
39
3Japanese (ja)
主イデアル整域上の有限生成加群の構造定理
21
4Catalan (ca)
Teorema d'estructura dels mòduls finitament generats sobre un domini d'ideals principals
16
5Russian (ru)
Структурная теорема для конечнопорождённых модулей над областями главных идеалов
13
6Ukrainian (uk)
Структурна теорема для скінченнопороджених модулів над областями головних ідеалів
4
7Vietnamese (vi)
Định lý cấu trúc cho các mô đun hữu hạn sinh trên một vành chính
1
More...

Scores

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

Quality measures

Interwikis

#LanguageValue
caCatalan
Teorema d'estructura dels mòduls finitament generats sobre un domini d'ideals principals
enEnglish
Structure theorem for finitely generated modules over a principal ideal domain
frFrench
Théorème des facteurs invariants
jaJapanese
主イデアル整域上の有限生成加群の構造定理
ruRussian
Структурная теорема для конечнопорождённых модулей над областями главных идеалов
ukUkrainian
Структурна теорема для скінченнопороджених модулів над областями головних ідеалів
viVietnamese
Định lý cấu trúc cho các mô đun hữu hạn sinh trên một vành chính

Popularity rank trends

Best Rank English:
#263216
01.2015
Global:
#418096
01.2015

AI rank trends

Best Rank English:
#70585
05.2009
Global:
#112974
07.2013

Languages comparison

Important global interconnections (July 2024 – June 2025)

Wikipedia readers most often find their way to information on Structure theorem for finitely generated modules over a principal ideal domain from Wikipedia articles about Finitely generated abelian group, Structure theorem, Smith normal form, Frobenius normal form and Principal ideal domain. Whereas reading the article about Structure theorem for finitely generated modules over a principal ideal domain people most often go to Wikipedia articles on Finitely generated abelian group, Primary decomposition, Principal ideal domain, Smith normal form and Finitely generated module.

Cumulative results of quality and popularity of the Wikipedia article

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

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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