- J-STAGE home
- /
- Journal of the Mathematical So ...
- /
- Volume 48 (1996) Issue 4
- /
- Article overview
On a normal integral bases problem over cyclotomic Zp-extensions
JOURNAL
FREE ACCESS
1996 Volume 48 Issue 4 Pages 689-703
Details
- Published: 1996 Received: October 28, 1994 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
-
Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J. Brinkhuis, On the Galois module structure over CM-fields, Manuscripta Math., 75 (1992), 333-347.
2) A. Brumer, On the units of algebraic number fields, Mathematika, 14 (1967), 121-124.
3) L.N. Childs, The group of unramified Kummer extensions of prime degree, Proc. London Math. Soc., 35 (1977), 407-422.
4) J. Coates, p-adic L-functions and Iwasawa's theory, Algebraic Number Fields, Durham Symposium 1975, (ed. A. Fröhlich), Academic Press, London, 1977, pp. 269-353.
5) B. Ferrero and L.C. Washington, The Iwasawa invariant μp vanishes for abelian number fields, Ann. of Math., 109 (1979), 377-395.
6) T. Fukuda and K. Komatsu, On Zp-extensions of real quadratic fields, J. Math. Soc. Japan, 38 (1986), 95-102.
7) T. Fukuda, Iwasawa λ-invariants of imaginary quadratic fields, J. College Industrial Technology Nihon Univ., 27 (1994), 35-88, (Corrigendum to appear in ibid.).
8) R. Gillard, Remarques sur les unités cyclotomiques et unités elliptiques, J. Number Theory, 11 (1979), 21-48.
9) R. Gillard, Unités cyclotomiques, unités semi-locales et Zl-extensions, Ann. Inst. Fourier, 29-1 (1979), 49-79.
10) R. Gillard, Unités cyclotomiques, unités semi-locales et Zl-extensions II, Ann. Inst. Fourier, 29-4 (1979), 1-15.
11) R. Greenberg, On the Iwasawa invariants of totally real number fields, Amer. J. Math., 98 (1976), 263-284.
12) R. Greenberg, On p-adic L-functions and cyclotomic fields, Nagoya Math. J., 67 (1977), 139-158.
13) H. Hasse, Über die Klassenzahl Abelscher Zahlkorper, Akademie-Verlag, 1952.
14) H. Ichimura, On a relative normal integral basis problem over abelian number fields, Proc. Japan Acad., 69 (1993), 413-416.
15) H. Ichimura, On p-adic L-functions and normal basis of rings of integers, J. Reine Angew. Math., 462 (1995), 169-184.
16) K. Iwasawa, A note on class numbers of algebraic number fields, Abh. Math. Sem. Univ. Hamburg, 20 (1956), 257-258.
17) K. Iwasawa, On some modules in the theory of cyclotomic fields, J. Math. Soc. Japan, 16 (1964), 42-82.
18) K. Iwasawa, Lectures on p-adic L-functions, Ann. of Math. Studies, 74, Princeton Univ. Press, 1972.
19) K. Iwasawa, On Zl-extensions of algebraic number fields, Ann. of Math., 98 (1973), 246-326.
20) K. Iwasawa, A note on cyclotomic fields, Invent. Math., 36 (1976), 115-123.
21) J.S. Kraft, Iwasawa invariants of CM fields, J. Number Theory, 32 (1989), 65-77.
22) B. Mazur and A. Wiles, Class fields of abelian extensions of Q, Invent. Math., 76 (1984), 179-330.
23) H. Taya, On the Iwasawa λ-invariants of real quadratic fields, Tokyo J. Math., 16 (1993), 121-130.
24) M.J, Taylor, The Galois module structure of certain arithmetic principal homogeneous spaces, J. Algebra, 153 (1992), 203-214.
25) L.C. Washington, Introduction to Cyclotomic Fields, Springer-Verlag, 1982.
Right : [1] J. Brinkhuis, On the Galois module structure over CM-fields, Manuscripta Math., 75 (1992), 333-347.
[2] A. Brumer, On the units of algebraic number fields, Mathematika, 14 (1967), 121-124.
[3] L. N. Childs, The group of unramified Kummer extensions of prime degree, Proc. London Math. Soc., 35 (1977), 407-422.
[4] J. Coates, p-adic L-functions and Iwasawa's theory, Algebraic Number Fields, Durham Symposium 1975, (ed. A. Fröhlich), Academic Press, London, 1977, pp. 269-353.
[5] B. Ferrero and L. C. Washington, The Iwasawa invariant μp vanishes for abelian number fields, Ann. of Math., 109 (1979), 377-395.
[6] T. Fukuda and K. Komatsu, On Zp-extensions of real quadratic fields, J. Math. Soc. Japan, 38 (1986), 95-102.
[7] T. Fukuda, Iwasawa λ-invariants of imaginary quadratic fields, J. College Industrial Technology Nihon Univ., 27 (1994), 35-88, (Corrigendum to appear in ibid.).
[8] R. Gillard, Remarques sur les unités cyclotomiques et unités elliptiques, J. Number Theory, 11 (1979), 21-48.
[9] R. Gillard, Unités cyclotomiques, unités semi-locales et Zl-extensions, Ann. Inst. Fourier, 29-1 (1979), 49-79.
[10] R. Gillard, Unités cyclotomiques, unités semi-locales et Zl-extensions II, Ann. Inst. Fourier, 29-4 (1979), 1-15.
[11] R. Greenberg, On the Iwasawa invariants of totally real number fields, Amer. J. Math., 98 (1976), 263-284.
[12] R. Greenberg, On p-adic L-functions and cyclotomic fields, Nagoya Math. J., 67 (1977), 139-158.
[13] H. Hasse, Über die Klassenzahl Abelscher Zahlkorper, Akademie-Verlag, 1952.
[14] H. Ichimura, On a relative normal integral basis problem over abelian number fields, Proc. Japan Acad., 69 (1993), 413-416.
[15] H. Ichimura, On p-adic L-functions and normal basis of rings of integers, J. Reine Angew. Math., 462 (1995), 169-184.
[16] K. Iwasawa, A note on class numbers of algebraic number fields, Abh. Math. Sem. Univ. Hamburg, 20 (1956), 257-258.
[17] K. Iwasawa, On some modules in the theory of cyclotomic fields, J. Math. Soc. Japan, 16 (1964), 42-82.
[18] K. Iwasawa, Lectures on p-adic L-functions, Ann. of Math. Studies, 74, Princeton Univ. Press, 1972.
[19] K. Iwasawa, On Zl-extensions of algebraic number fields, Ann. of Math., 98 (1973), 246-326.
[20] K. Iwasawa, A note on cyclotomic fields, Invent. Math., 36 (1976), 115-123.
[21] J. S. Kraft, Iwasawa invariants of CM fields, J. Number Theory, 32 (1989), 65-77.
[22] B. Mazur and A. Wiles, Class fields of abelian extensions of Q, Invent. Math., 76 (1984), 179-330.
[23] H. Taya, On the Iwasawa λ-invariants of real quadratic fields, Tokyo J. Math., 16 (1993), 121-130.
[24] M. J, Taylor, The Galois module structure of certain arithmetic principal homogeneous spaces, J. Algebra, 153 (1992), 203-214.
[25] L. C. Washington, Introduction to Cyclotomic Fields, Springer-Verlag, 1982.
Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -
Download PDF (1297K)
Download citation
RIS
BIB TEX
Text
How to download citation
Contact us
(compatible with EndNote, Reference Manager, ProCite, RefWorks)
(compatible with BibDesk, LaTeX)
Article 1st page
