Minimal polynomial (field theory)

Minimal polynomial - given an element α of a field extension E/F, the unique monic polynomial p∈F[x] of minimal degree such that p(α) = 0. Article "Minimal polynomial (field theory)" in English Wikipedia has 22.7 points for quality (as of July 1, 2025). The article contains 0 references and 13 sections.

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

Since the creation of article "Minimal polynomial (field theory)", its content was written by 36 registered users of English Wikipedia and edited by 225 registered Wikipedia users in all languages.

The article is cited 82 times in English Wikipedia and cited 381 times in all languages.

The highest Authors Interest rank from 2001:

• Local (English): #74243 in February 2014
• Global: #25512 in April 2004

The highest popularity rank from 2008:

• Local (English): #258942 in January 2015
• Global: #255627 in January 2015

There are 18 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	Catalan (ca) Polinomi minimal		39.5321
2	Spanish (es) Polinomio mínimo (teoría de cuerpos)		22.8178
3	English (en) Minimal polynomial (field theory)		22.689
4	French (fr) Polynôme minimal (théorie des corps)		21.0618
5	Hebrew (he) פולינום מינימלי		13.3777
6	Arabic (ar) متعددة الحدود الدنيا (نظرية الحقول)		12.1611
7	Romanian (ro) Polinom minimal		11.4956
8	Dutch (nl) Minimale polynoom (galoistheorie)		11.4411
9	Czech (cs) Minimální polynom (teorie těles)		7.2528
10	Vietnamese (vi) Đa thức tối tiểu (lý thuyết trường)		6.5489

More...

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

The most popular language versions of the article "Minimal polynomial (field theory)" in all the time

#	Language	Popularity award	Relative popularity
1	English (en) Minimal polynomial (field theory)		318 683
2	German (de) Minimalpolynom (Körpertheorie)		212 917
3	Hebrew (he) פולינום מינימלי		65 961
4	French (fr) Polynôme minimal (théorie des corps)		49 901
5	Chinese (zh) 極小多項式		49 361
6	Russian (ru) Минимальный многочлен алгебраического элемента		38 070
7	Japanese (ja) 最小多項式 (体論)		26 827
8	Portuguese (pt) Polinômio mínimo		19 018
9	Vietnamese (vi) Đa thức tối tiểu (lý thuyết trường)		7 033
10	Greek (el) Ελάχιστο πολυώνυμο		5 959

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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 "Minimal polynomial (field theory)" in June 2025

#	Language	Popularity award	Relative popularity
1	English (en) Minimal polynomial (field theory)		1 574
2	German (de) Minimalpolynom (Körpertheorie)		289
3	French (fr) Polynôme minimal (théorie des corps)		198
4	Russian (ru) Минимальный многочлен алгебраического элемента		196
5	Hebrew (he) פולינום מינימלי		173
6	Chinese (zh) 極小多項式		158
7	Japanese (ja) 最小多項式 (体論)		123
8	Vietnamese (vi) Đa thức tối tiểu (lý thuyết trường)		72
9	Portuguese (pt) Polinômio mínimo		45
10	Spanish (es) Polinomio mínimo (teoría de cuerpos)		23

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

Language versions of the article "Minimal polynomial (field theory)" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.

#	Language	AI award	Relative AI
1	German (de) Minimalpolynom (Körpertheorie)		60
2	French (fr) Polynôme minimal (théorie des corps)		37
3	English (en) Minimal polynomial (field theory)		36
4	Hebrew (he) פולינום מינימלי		31
5	Dutch (nl) Minimale polynoom (galoistheorie)		13
6	Catalan (ca) Polinomi minimal		9
7	Greek (el) Ελάχιστο πολυώνυμο		9
8	Chinese (zh) 極小多項式		9
9	Russian (ru) Минимальный многочлен алгебраического элемента		4
10	Vietnamese (vi) Đa thức tối tiểu (lý thuyết trường)		4

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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 "Minimal polynomial (field theory)" with the highest AI in June 2025

#	Language	AI award	Relative AI
1	Arabic (ar) متعددة الحدود الدنيا (نظرية الحقول)		0
2	Catalan (ca) Polinomi minimal		0
3	Czech (cs) Minimální polynom (teorie těles)		0
4	German (de) Minimalpolynom (Körpertheorie)		0
5	Greek (el) Ελάχιστο πολυώνυμο		0
6	English (en) Minimal polynomial (field theory)		0
7	Spanish (es) Polinomio mínimo (teoría de cuerpos)		0
8	Persian (fa) چندجمله‌ای کمینه (نظریه میدان)		0
9	French (fr) Polynôme minimal (théorie des corps)		0
10	Hebrew (he) פולינום מינימלי		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 "Minimal polynomial (field theory)" with the highest Citation Index (CI)

#	Language	CI award	Relative CI
1	English (en) Minimal polynomial (field theory)		82
2	French (fr) Polynôme minimal (théorie des corps)		62
3	Hebrew (he) פולינום מינימלי		36
4	Chinese (zh) 極小多項式		34
5	German (de) Minimalpolynom (Körpertheorie)		31
6	Japanese (ja) 最小多項式 (体論)		26
7	Russian (ru) Минимальный многочлен алгебраического элемента		25
8	Ukrainian (uk) Мінімальний многочлен (теорія полів)		19
9	Romanian (ro) Polinom minimal		14
10	Spanish (es) Polinomio mínimo (teoría de cuerpos)		13

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#	Language	Value
ar	Arabic متعددة الحدود الدنيا (نظرية الحقول)
ca	Catalan Polinomi minimal
cs	Czech Minimální polynom (teorie těles)
de	German Minimalpolynom (Körpertheorie)
el	Greek Ελάχιστο πολυώνυμο
en	English Minimal polynomial (field theory)
es	Spanish Polinomio mínimo (teoría de cuerpos)
fa	Persian چندجمله‌ای کمینه (نظریه میدان)
fr	French Polynôme minimal (théorie des corps)
he	Hebrew פולינום מינימלי
ja	Japanese 最小多項式 (体論)
nl	Dutch Minimale polynoom (galoistheorie)
pt	Portuguese Polinômio mínimo
ro	Romanian Polinom minimal
ru	Russian Минимальный многочлен алгебраического элемента
uk	Ukrainian Мінімальний многочлен (теорія полів)
vi	Vietnamese Đa thức tối tiểu (lý thuyết trường)
zh	Chinese 極小多項式

Best Rank

English: #258942 01.2015

Global: #255627 01.2015

Best Rank

English: #74243 02.2014

Global: #25512 04.2004

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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