algebraic number field
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English
[edit]Noun
[edit]algebraic number field (plural algebraic number fields)
- (mathematics, 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.
- 1984, Alan Baker, A Concise Introduction to the Theory of Numbers, Cambridge University Press, page 61:
- 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.
- 1989, M. Pohst, H. Zassenhaus, Algorithmic Algebraic Number Theory, 1st paperback edition, Cambridge University Press, published 1997, page 381:
- 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.
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[edit]Further reading
[edit]- Algebraic number ring on Wikipedia.Wikipedia
- Algebraic number theory on Wikipedia.Wikipedia