noun
Meaning 1
A number field that is an extension field of degree two over the rational numbers.
Definition source: English Wiktionary via Wiktextract
Qualifier: algebraic number theory
Examples
- 1985, Erich Kaltofen, Heinrich Rolletschek, Arithmetic in Quadratic Fields with Unique Factorization, Bob F. Caviness (editor), EUROCAL '85: European Conference on Computer Algebra, Proceedings, Volume 2, Springer, LNCS 204, page 279, In a quadratic field mathbf Q(√), D a squarefree integer, with class number 1 any algebraic integer can be decomposed uniquely into primes but for only 21 domains Euclidean algorithms are known.
- 2007, H. M. Stark, The Gauss Class-Number Problems, William Duke, Yuri Tschinkel (editors), Analytic Number Theory: A Tribute to Gauss and Dirichlet, American Mathematical Society, Clay Mathematics Institute, page 247, Since Dedekind's time, these conjectures have been phrased in the language of quadratic fields. [...] Throughout this paper, k= Q (√d) will be a quadratic field of discriminant d and h(k) or sometimes h(d) will be the class-number of k.
Meaning relationships
Synonyms: none provided
Antonyms: none provided