Effective determination of the decomposition of the rational primes in a cubic field
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- by Pascual Llorente and Enric Nart PDF
- Proc. Amer. Math. Soc. 87 (1983), 579-585 Request permission
Abstract:
The decomposition of the rational primes in a cubic field $K$ is determined in terms of the coefficients of a defining polynomial of $K$. As a consequence, the discriminant $D$ of $K$ is straightforwardly computed and the cubic fields with index $i(K) = 2$ are easily characterized.References
-
M. Bauer, Zur allgemeinen Theorie der algebraischen Grössen, J. Reine Angew. Math. 132 (1907), 21-32.
R. Dedekind, Über den Zusammenhang zwischen der Theorie der Ideale und der höheren Kongruenzen, Abh. Kgl. Ges. Wiss. Göttingen 23 (1878), 1-23.
- B. N. Delone and D. K. Faddeev, The theory of irrationalities of the third degree, Translations of Mathematical Monographs, Vol. 10, American Mathematical Society, Providence, R.I., 1964. MR 0160744
- H. T. Engstrom, On the common index divisors of an algebraic field, Trans. Amer. Math. Soc. 32 (1930), no. 2, 223–237. MR 1501535, DOI 10.1090/S0002-9947-1930-1501535-0
- Helmut Hasse, Arithmetische Theorie der kubischen Zahlkörper auf klassenkörpertheoretischer Grundlage, Math. Z. 31 (1930), no. 1, 565–582 (German). MR 1545136, DOI 10.1007/BF01246435
- Jacques Martinet and Jean-Jacques Payan, Sur les extensions cubiques non-Galoisiennes des rattionnels et leur clôture Galoisienne, J. Reine Angew. Math. 228 (1967), 15–37 (French). MR 227137
- Władysław Narkiewicz, Elementary and analytic theory of algebraic numbers, Monografie Matematyczne, Tom 57, PWN—Polish Scientific Publishers, Warsaw, 1974. MR 0347767
- Leonard Tornheim, Minimal basis and inessential discriminant divisors for a cubic field, Pacific J. Math. 5 (1955), 623–631. MR 73637
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 87 (1983), 579-585
- MSC: Primary 12A30; Secondary 12A50
- DOI: https://doi.org/10.1090/S0002-9939-1983-0687621-6
- MathSciNet review: 687621