Concept information
Preferred term
cyclotomic field
Definition(s)
-
In number theory, a cyclotomic field is a number field obtained by adjoining a complex root of unity to Q, the field of rational numbers. Cyclotomic fields played a crucial role in the development of modern algebra and number theory because of their relation with Fermat's Last Theorem. It was in the process of his deep investigations of the arithmetic of these fields (for prime n) – and more precisely, because of the failure of unique factorization in their rings of integers – that Ernst Kummer first introduced the concept of an ideal number and proved his celebrated congruences.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Cyclotomic_field)
Broader concept(s)
Narrower concept(s)
- Chowla-Mordell theorem
- cyclotomic polynomial
- Eisenstein integer
- Gaussian integer
- Gaussian period
- Gaussian rational
- Gauss sum
- Herbrand-Ribet theorem
- Hilbert-Speiser theorem
- Iwasawa theory
- Jacobi sum
- Kronecker-Weber theorem
- Kummer theory
- Kummer-Vandiver conjecture
- regular prime
- root of unity
- Stickelberger's theorem
- Thaine's theorem
- tower of fields
In other languages
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French
URI
http://data.loterre.fr/ark:/67375/PSR-DQMTBLQT-5
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