Class field theory

The fifth roots of unity in the complex plane. Adjoining these roots to the rational numbers generates an abelian extension.

In mathematics, class field theory is a major branch of algebraic number theory that studies abelian extensions of number fields and function fields of curves over finite fields and arithmetic properties of such abelian extensions. A general name for such fields is global fields, or one-dimensional global fields.

单词	Maximal abelian extension
释义	Maximal abelian extension 英语百科 Class field theory In mathematics, class field theory is a major branch of algebraic number theory that studies abelian extensions of number fields and function fields of curves over finite fields and arithmetic properties of such abelian extensions. A general name for such fields is global fields, or one-dimensional global fields.
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Maximal abelian extension

Class field theory