| Information | |
|---|---|
| has gloss | eng: In number theory, a cyclotomic field is a number field obtained by adjoining a complex primitive root of unity to Q, the field of rational numbers. The n-th cyclotomic field Q(ζn) (with n > 2) is obtained by adjoining a primitive n-th root of unity ζn to the rational numbers. |
| lexicalization | eng: Cyclotomic fields |
| lexicalization | eng: cyclotomic field |
| subclass of | (noun) a piece of land cleared of trees and usually enclosed; "he planted a field of wheat" field |
| has instance | e/Chowla-Mordell theorem |
| has instance | e/Cyclotomic unit |
| has instance | e/Gauss sum |
| has instance | e/Gaussian period |
| has instance | e/Gaussian rational |
| has instance | e/Hasse-Davenport relation |
| has instance | e/Herbrand-Ribet theorem |
| has instance | e/Hilbert-Speiser theorem |
| has instance | e/Iwasawa theory |
| has instance | e/Jacobi sum |
| has instance | e/Kummer ring |
| has instance | e/Kummer sum |
| has instance | e/Kummer theory |
| has instance | e/Quadratic Gauss sum |
| has instance | e/Stickelberger's theorem |
| Meaning | |
|---|---|
| German | |
| has gloss | deu: Kreisteilungskörper sind Studienobjekte des mathematischen Teilgebietes der algebraischen Zahlentheorie. Sie sind in gewisser Hinsicht besonders einfache Verallgemeinerungen des Körpers der rationalen Zahlen. |
| lexicalization | deu: Kreisteilungskörper |
| French | |
| has gloss | fra: En théorie algébrique des nombres, on appelle extension cyclotomique du corps \mathbbQ} des nombres rationnels, les surcorps de la forme \mathbbQ}(\zeta_n) où \zeta_n est une racine primitive nème de l'unité ; cette appellation provient de ce que ces extensions sont des corps de décomposition des polynômes cyclotomiques. |
| lexicalization | fra: Corps cyclotomiques |
| lexicalization | fra: extension cyclotomique |
| Japanese | |
| has gloss | jpn: 円分体 (えんぶんたい、) は、有理数体に、1 の m(>2) 乗根 \scriptstyle\zeta(\ne\pm 1) を添加した代数体である。 円分体およびその部分体のことを円体ともいう。 |
| lexicalization | jpn: 円分体 |
| Dutch | |
| has gloss | nld: In de algebraïsche getaltheorie, een deelgebied van de wiskunde, is een cyclotomisch veld een getallenlichaam, dat wordt verkregen door een complexe primitieve eenheidswortel toe te voegen aanaan Q, het veld van de rationale getallen. |
| lexicalization | nld: Cyclotomisch veld |
| Portuguese | |
| has gloss | por: Em teoria dos números, um corpo ciclotômico é um corpo numérico obtido por agregar uma raiz da unidade complexa a Q, o corpo dos números racionais. O corpo ciclotômico n-ésimo Q(ζn) (com n > 2) é obtido por agregar uma raiz de unidade n-ésima primitiva ζn aos números racionais. |
| lexicalization | por: corpo ciclotômico |
| Chinese | |
| has gloss | zho: 在数论中，分圆域是在有理数域 \mathbbQ} 中添加复数单位根进行扩张而得到的数域。将 n 次单位根 \zeta_n 加入而得到的分圆域称为 n 次分圆域，记作 \mathbbQ}(\zeta_n}) 。 |
| lexicalization | zho: 分圆域 |
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