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On cyclic biquadratic fields related to a problem of Hasse. (English) Zbl 0482.12001


MSC:

11R04 Algebraic numbers; rings of algebraic integers
11R16 Cubic and quartic extensions
11R18 Cyclotomic extensions
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References:

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[8] Hasse, H.: Über die Klassenzahl abelscher Zahlkörper. Berlin: Akademie-Verlag. 1952. · Zbl 0063.01966
[9] Hasse, H.: Arithmetische Bestimmung von Grundeinheit und Klassenzahl in zyklischen kubischen und biquadratischen Zahlkörpern. Abh. Deutsch. Akad. Wiss. Berlin, Math.-Nat. Kl.1950, Nr. 2, 3-95. · Zbl 0035.30502
[10] Hasse, H.: Vorlesungen über Zahlentheorie. Berlin-Göttingen-Heidelberg-New York: Springer. 1964. · Zbl 0168.26704
[11] Hasse, H.: Zahlentheorie. Berlin: Akademie-Verlag. 1969.
[12] Hasse, H.: Zahlbericht. Würzburg-Wien: Physica-Verlag. 1970.
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[14] Liang, J. J.: On the integral basis of the maximal real subfield of a cyclotomic field. J. Reine Angew. Math.286/287, 223-226 (1976). · Zbl 0335.12015 · doi:10.1515/crll.1976.286-287.223
[15] Nakahara, T.: Examples of algebraic number fields which have not unramified extensions. Rep. Fac. Sci. Engrg. Saga Univ. Math.1, 1-8 (1973). · Zbl 0258.12003
[16] Nakahara, T.: On the unessential factor of the discriminant of a cyclic biquadratic field. (In Japanese.) In: Algebraic Number theory. Proc. Sympos. Kyushu Univ., Fukuoka, 1978, pp. 34-43.
[17] Nakahara, T.: On a power basis of the integer ring in an abelian biquadratic field. (In Japanese.) RIMS K?ky?roku371, 31-46 (1979).
[18] Narkiewicz, W.: Elementary and Analytic Theory of Algebraic Numbers. Warsaw: Polish Scientific Publ. 1974. · Zbl 0276.12002
[19] Payan, J. J.: Sur les classes ambigues et les ordres monogènes d’une extension cyclique de degré premier impair surQ ou sur un corps quadratique imaginaire. Ark. Mat.11, 239-244 (1973). · Zbl 0269.12003 · doi:10.1007/BF02388520
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