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A number field obtained by adjoining a primitive root of unity to the field of rational numbers.
Definition source: English Wiktionary via Wiktextract
Qualifier: algebraic number theory
Topics: mathematics, number-theory, sciences
Examples
- A cyclotomic field is the splitting field of the cyclotomic polynomial #92;Phi#95;n(x)#61;#92;prod#95;#92;stackrel#123;1#92;lek#92;len#125;#123;#92;gcd(k,n)#61;1#125;#92;left(x-e#123;#92;frac#123;2k#92;pii#125;#123;n
Meaning relationships
Synonyms: none provided
Antonyms: none provided
No etymology was provided for this word.
Across languages
Translations
5 source translations are retained for this English entry.
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German:
Kreisteilungskörper
— extension field of the rational numbers formed by adjoining a primitive root of unity
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German:
zyklotomische Körper
— extension field of the rational numbers formed by adjoining a primitive root of unity
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Italian:
campo ciclotomico
— extension field of the rational numbers formed by adjoining a primitive root of unity
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Polish:
ciało cyklotomiczne
— extension field of the rational numbers formed by adjoining a primitive root of unity
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Spanish:
cuerpo ciclotómico
— extension field of the rational numbers formed by adjoining a primitive root of unity
