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An integral basis for algebraic fields

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Abstract

Let A be a principal ideal domain, K be the quotient field of A, and let L be a cubic extension of K. In this paper we establish the existence of a special type of integral basis of the field L over K which is a generalization of the integral basis of Voronoi for cubic extensions of the field Q of rational numbers.

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Literature cited

  1. B. M. Urazbaev, “On the form of a fundamental basis,” Izv. Akad. Nauk Kaz. SSR, Ser. Matem i Mekhan.,1, 56–68 (1947).

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  2. G. F. Voronoi, “On integral algebraic numbers depending on a root of a third degree equation,” Collection of Works, Vol. 1 [in Russian], Kiev (1952).

  3. Wada Hideo, “On cubic Galois extensions of Q(√−3), Proc. Jap. Acad.,46, No. 5, 397–400 (1970).

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Authors and Affiliations

  1. Cuban State University, USSR

    É. A. Sergeev

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  1. É. A. Sergeev
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Translated from Matematicheskie Zametki, Vol. 13, No. 2, pp. 229–234, February, 1973.

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Sergeev, É.A. An integral basis for algebraic fields. Mathematical Notes of the Academy of Sciences of the USSR 13, 137–140 (1973). https://doi.org/10.1007/BF01094231

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  • DOI: https://doi.org/10.1007/BF01094231

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