Algebraic number fields with the discriminant equal to that of a quadratic number field

Takeshi KONDO

doi:10.2969/jmsj/04710031

Takeshi KONDO

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JOURNAL FREE ACCESS

1995 Volume 47 Issue 1 Pages 31-36

DOI https://doi.org/10.2969/jmsj/04710031

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Published: 1995 Received: May 12, 1993 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : F1) G. Fujisaki, On an example of an unramified Galois extension, (in Japanese), Sûgaku, 9 (1957), 97-99,
F2) G. Fujisaki, Introduction to Algebraic Number Theory, (in Japanese), Shoukabou, 1975.
K) K. Komatsu, Square-free discriminants and affect-free equations, Tokyo J. Math., 14 (1991), 57-60.
M) E. Maus, Computation of integral bases in certain S_n extensions of Q, J. Symbolic Comput., 4 (1987), 99-102.
N) J. Nakagawa, On the Galois group of a number field with square free discriminant, Comment. Math. Univ. St. Paul., 37 (1988), 95-98.
O) H. Osaka, The Galois groups of the polynomials Xⁿ+aX^l+b, J. Number Theory, 25(1987), 230-238.
S) R. P. Stauduhar, The determination of Galois groups, Math. Comp., 27 (1973), 981-996.
U) K. Uchida, Unramified extensions of quadratic number fields, I, Tohoku Math. J., 7 (1970), 138-140.
W) B. L. van der Waerden, Die Zerlegengs-und Trägheitsgruppe als Permutations-gruppen, Math. Ann., 111 (1935), 731-733.
YK) K. Yamazaki, The computation of Galois groups, (in Japanese), Report of Symposium at Osaka Univ., (ed. T. Kondo), 1981, pp. 9-57.
YY) Y. Yamamoto, On ramified Galois extensions of quadratic number fields, Osaka J. Math., 7 (1970), 57-76.
Y1) K. Yamamura, On unramified Galois extensions of real quadratic number fields, Osaka J. Math., 23 (1986), 471-478.
Y2) K. Yamamura, Some analogue of Hilbert's irreducibility theorem and the distribution of algebraic number fields, J. Fac. Sci. Univ. Tokyo, 38 (1991), 99-135.

Right : [F1] G. Fujisaki, On an example of an unramified Galois extension, (in Japanese), Sûgaku, 9 (1957), 97-99,
[F2] G. Fujisaki, Introduction to Algebraic Number Theory, (in Japanese), Shoukabou, 1975.
[K] K. Komatsu, Square-free discriminants and affect-free equations, Tokyo J. Math., 14 (1991), 57-60.
[M] E. Maus, Computation of integral bases in certain S_n extensions of Q, J. Symbolic Comput., 4 (1987), 99-102.
[N] J. Nakagawa, On the Galois group of a number field with square free discriminant, Comment. Math. Univ. St. Paul., 37 (1988), 95-98.
[O] H. Osaka, The Galois groups of the polynomials Xⁿ+aX^l+b, J. Number Theory, 25 (1987), 230-238.
[S] R. P. Stauduhar, The determination of Galois groups, Math. Comp., 27 (1973), 981-996.
[U] K. Uchida, Unramified extensions of quadratic number fields, I, Tôhoku Math. J., 7 (1970), 138-140.
[W] B. L. van der Waerden, Die Zerlegengs-und Trägheitsgruppe als Permutations-gruppen, Math. Ann., 111 (1935), 731-733.
[YK] K. Yamazaki, The computation of Galois groups, (in Japanese), Report of Symposium at Osaka Univ., (ed. T. Kondo), 1981, pp. 9-57.
[YY] Y. Yamamoto, On ramified Galois extensions of quadratic number fields, Osaka J. Math., 7 (1970), 57-76.
[Y1] K. Yamamura, On unramified Galois extensions of real quadratic number fields, Osaka J. Math., 23 (1986), 471-478.
[Y2] K. Yamamura, Some analogue of Hilbert's irreducibility theorem and the distribution of algebraic number fields, J. Fac. Sci. Univ. Tokyo, 38 (1991), 99-135.

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