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On the group of units of number fields of degree 2 and 4. (Sur le groupe des unités de corps de nombres de degré 2 et 4.) (French. English summary) Zbl 1196.11150

Summary: We give under certain hypotheses, a fundamental system of units of the field \(K=\mathbb Q(\omega)\) and its quadratic subfield, where \(\omega\) is a root of the polynomial \(f(X)=X^4 +d^{-2} M_6 X^2 -M_4\), with \(M_6 =D^6 +6D^4 d+9D^2 d^2 +2d^3\), \(M_4 =D^4 +4D^2 d+2d^2\), \(d, D\in\mathbb N\), \(d\mid D\).

MSC:

11R27 Units and factorization
11R11 Quadratic extensions
11R16 Cubic and quartic extensions
11R04 Algebraic numbers; rings of algebraic integers
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References:

[1] L. Bernstein, Fundamental units and cycles in period of real quadratic number fields, Part I. Pac. J. Math. 68 No. 1 (1976), 37-61 ; and J. Number Theory 8 (1976), 446-491. · Zbl 0335.10010
[2] L. Bernstein, Fundamental units and cycles in period of real quadratic number fields. Part II, Pac. J. Math. 68 No. 1 (1976), 63-78. · Zbl 0335.10011
[3] N. Bourbaki, Algèbre, chapitre 5, corps commutatifs \(, (2^{eme}\) édition). Hermann, Paris, 1959.
[4] T. W. Hungerford, Algebra. Holt, Rinehart and Winston, Inc., New York, 1974. · Zbl 0293.12001
[5] C. Levesque, Truncated units. J. Number Theory 41 No. 1 (1992), 48-68. · Zbl 0759.11038
[6] W. Ljunggren, Über die Lösung einiger unbestimmten Gleichungen vierten Grades. Avh. Norske Vid.-Akad. Oslo, I. Mat.-Nat. Kl. (1935), 1-35. · Zbl 0011.14701
[7] H.-J. Stender, “Verstummelte” Grundeinheiten für biquadratische und bikubische Zahlkörper. Math. Ann. 232 (1982), 55-64. · Zbl 0372.12009
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