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algebraic number field

noun

Definitions

  1. A field which includes the rational numbers and has finite dimension as a vector space…

    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.
    • In this section we consider the maximal order of an algebraic number field and discuss the most important consequences which follow from the fact of it being a Dedekind ring.

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sense glosses and etymology drawn from English Wiktionary · source · CC-BY-SA