Algebraic number field

In mathematics, an algebraic number field (or simply number field) is a finite (and therefore algebraic) field extension of the rational numbers Q. That is, it is a field which contains Q and has finite dimension when considered as a vector space over Q.

Related Topics:
Mathematics - Algebraic - Field extension - Rational number - Field - Dimension - Vector space

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The study of algebraic number fields, and these days also of infinite algebraic extensions of the rational number field, is the central topic of algebraic number theory.

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See in particular:

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• quadratic field
• cyclotomic field
• additive polynomial
• Ideal class group
• Dirichlet's unit theorem
• local field
• global field
• abelian extension
• Kummer extension
• reciprocity law
• class field theory
• Brauer group
• Iwasawa theory
• Dedekind zeta function.