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A principal ideal theorem in the genus field. (English) Zbl 0243.12003


MSC:

11R23 Iwasawa theory
11R37 Class field theory
Full Text: DOI

References:

[1] E. ARTIN, Idealklassen in Oberkorpern und allgemeines Reziprozitatsgesetz, Hamb. Abh., 7 (1930). · JFM 55.0699.01
[2] PH. FURTWANGLER, Beweis des Hauptidealsatzes, ibid
[3] S. IYANAGA, Uber den allgemeinen Hauptidealsatzs, Jap. Journ., 7(1931) Zentralblatt MATH: · Zbl 0002.12101
[4] S. IYANAGA, Zum Beweis des Hauptidealsatzes, Crelle. 170(1934) · JFM 56.0858.02
[5] F. TERADA, On a generalization of tbe principal ideal theorem, Thoku Math. J., 1(1949) · Zbl 0041.17203 · doi:10.2748/tmj/1178245697
[6] H. HASSE, Zur Geschlechtertheorie in quadratischen Zahlkorpern, J. Math. Soc. Japan, 3(1951). · Zbl 0043.04002 · doi:10.2969/jmsj/00310045
[7] H. LEOPOLDT, Zur Geschlechtertheorie in abelschen Zahlkorpern, Math. Nachr., 9(1953) · Zbl 0053.35502 · doi:10.1002/mana.19530090604
[8] F. TERADA. A generalization of the principal ideal theorem, J. Math. Soc. Japan, 7(1955) · Zbl 0068.03401 · doi:10.2969/jmsj/00750530
[9] T. TANNAKA, A generalized principal ideal theorem and a proof of a conjecture of Deuring, Ann. of Math. No. 67, 3(1958). JSTOR: · Zbl 0081.26705 · doi:10.2307/1969872
[10] H. YOKOI, On the number of a relatively cyclic number field, Nagoya Math, J., 29(1967) · Zbl 0166.05803
[11] J. W. S. CASSELS AND A FROHLICH, Algebraic Number Theory, Academic Press, Londo and New York, (1967).
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