## KONDO : Algebraic number fields with the discriminant equal to that of a quadratic number field

Thuswaldner, On the topological structure of fractal tilings generated by quadratic number systems , Comput. Brunotte, On trinomial bases of radix representations of algebraic integers , Acta Sci.

- Discriminant of an algebraic number field.
- Algebraic Number Fields: Second Edition.
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Szeged , 67 , — Szeged , 70 , — Gilbert, Radix representations of quadratic fields , J. Grossman, Number bases in quadratic fields , Studia Sci. Debrecen , 23 , — Szeged , 42 , 99— Szeged , 37 , — Knuth, An imaginary number system , Comm.

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ACM, 3 , — MR Szeged , 55 , — Szeged , 50 , — Lettl and A. Hamburg 65 , — Mignotte, A.

Friedman E Analytic formulas for the regulator of a number field. Friedman E Regulators and total positivity. Cambridge studies in advanced mathematics, vol Cambridge University Press, Cambridge. Garbanati D Class field theory summarized. Springer-Verlag, Berlin. Ellipses, Paris. Greenberg M An elementary proof of the Kronecker—Weber theorem. Am Math Mon — Publ Math Debr — Hagedorn TR General formulas for solving solvable sextic equations. Heegner K Diophantische Analysis und Modulfunktionen.

- Algebraic Number Fields | A Survey of Modern Algebra | Taylor & Francis Group.
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- Computing GCDs of Polynomials over Algebraic Number Fields - Microsoft Research.

Herz CS Construction of class fields. In: Seminar on complex multiplication. Lecture notes in math. Iwaniec H, Kowalski E Analytic number theory. Colloquium publications, vol Janusz G Algebraic number fields. Graduate studies in mathematics, vol 7, 2nd edn. Teubner, Leipzig. Lang S Algebra, 3rd edn.

## THE TATE MODULE FOR ALGEBRAIC NUMBER FIELDS

Lang S Algebraic number theory. GTM, vol , 2nd edn. Llorente P, Nart E Effective determination of the decomposition of the rational primes in a cubic field. This also shows, BTW, that the algebraic integers are closed under addition and multiplication: they are the eigenvalues of matrices with integer entries. I find another charming proof in Lecture on the theory of algebraic numbers by Hecke.

## Algebraic number

It is constructive in appearance, but is impractical in fact. A similar proof goes for products. Inform me of any ambiguity or error, thanks. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered.

Enlightening proof that the algebraic numbers form a field Ask Question. Asked 6 years, 6 months ago.

Active 6 years, 6 months ago. Viewed 7k times. Alex Becker Alex Becker If you specifically wanted to see why the constructive proof is not merely an accident, then see this link- after proving that the sum of algebraic numbers is algebraic in the usual way, they add: Now let us analyse the above argument a little.