Meaning of algebraic number field | Babel Free

Definitions

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

Equivalents

Examples

“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⟳.”

“2006, Andres Iglesias, Nobuki Takayama (editors), Mathematical Software - ICMS 2006: 2nd International Congress, Proceedings, Masayuki Noro, An Efficient Implementation for Computing Gröbner Bases over Algebraic Number⟳ Fields, Springer, LNCS 4151, page 99, If the operations over an algebraic number⟳ field are provided, we can apply⟳ [the] usual Buchberger algorithm over the field.”

CEFR level