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Witt equivalence classes of quartic number fields

Authors: Stanislav Jakubec and František Marko
Journal: Math. Comp. 58 (1992), 355-368
MSC: Primary 11E81; Secondary 11E08, 11E12, 11R16
MathSciNet review: 1094952
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Abstract: It has recently been established that there are exactly seven Witt equivalence classes of quadratic number fields, and then all quadratic and cubic number fields have been classified with respect to Witt equivalence. In this paper we have classified number fields of degree four. Using this classification, we have proved the Conjecture of Szymiczek about the representability of Witt equivalence classes by quadratic extensions of quadratic fields.

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  • [1] Z. I. Borevič and I. R. Šafarevič, Number theory, 3rd rev. ed., Nauka, Moscow, 1985. (Russian)
  • [2] J. W. S. Cassels and A. Fröhlich, Algebraic number theory, Proceeding of an instructional conference organized by the London Mathematical Society, Academic Press, London and New York, 1967. MR 0215665 (35:6500)
  • [3] B. N. Delone and D. K. Faddeev, Theory of irrationalities of the third degree, Trudy Mat. Inst. Steklov. 11 (1940); English transl., Transl. Math. Monographs, vol. 10, Amer. Math. Soc., Providence, R. I., 1964. MR 0004269 (2:349d)
  • [4] R. Fricke, Lehrbuch der Algebra, Vol. I, Vieweg, Braunschweig, 1924.
  • [5] W. Narkiewicz, Elementary and analytic theory of algebraic numbers, PWN, Warszawa, 1974. MR 0347767 (50:268)
  • [6] K. Petr, Bases of integers in algebraic number fields, Časopis Pěst. Mat. Fys. 5 (1935), 62-72. (Czech)
  • [7] K. Szymiczek, Witt equivalence of global fields, Comm. Algebra 19 (1991), 1125-1149. MR 1102331 (92d:11031)

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Article copyright: © Copyright 1992 American Mathematical Society

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