algebraic number field

Noun

algebraic number field (plural algebraic number fields)

1. (algebraic number theory) A field which includes the rational numbers and has finite dimension as a vector space over the rational numbers.
   • The study of algebraic number fields, and, more generally, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory.
   • Although we shall be concerned in the sequel only with quadratic fields, we shall nevertheless begin with a short discussion of the more general concept of an algebraic number field.1984, Alan Baker, A Concise Introduction to the Theory of Numbers, Cambridge University Press, page 61

   Synonyms:

   number field