Kronecker-Weber via Stickelberger

Franz Lemmermeyer[1]

  • [1] Department of Mathematics Bilkent University 06800 Bilkent, Ankara, Turkey

Journal de Théorie des Nombres de Bordeaux (2005)

  • Volume: 17, Issue: 2, page 555-558
  • ISSN: 1246-7405

Abstract

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In this note we give a new proof of the theorem of Kronecker-Weber based on Kummer theory and Stickelberger’s theorem.

How to cite

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Lemmermeyer, Franz. "Kronecker-Weber via Stickelberger." Journal de Théorie des Nombres de Bordeaux 17.2 (2005): 555-558. <http://eudml.org/doc/249466>.

@article{Lemmermeyer2005,
abstract = {In this note we give a new proof of the theorem of Kronecker-Weber based on Kummer theory and Stickelberger’s theorem.},
affiliation = {Department of Mathematics Bilkent University 06800 Bilkent, Ankara, Turkey},
author = {Lemmermeyer, Franz},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
number = {2},
pages = {555-558},
publisher = {Université Bordeaux 1},
title = {Kronecker-Weber via Stickelberger},
url = {http://eudml.org/doc/249466},
volume = {17},
year = {2005},
}

TY - JOUR
AU - Lemmermeyer, Franz
TI - Kronecker-Weber via Stickelberger
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2005
PB - Université Bordeaux 1
VL - 17
IS - 2
SP - 555
EP - 558
AB - In this note we give a new proof of the theorem of Kronecker-Weber based on Kummer theory and Stickelberger’s theorem.
LA - eng
UR - http://eudml.org/doc/249466
ER -

References

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  1. M.J. Greenberg, An elementary proof of the Kronecker-Weber theorem. Amer. Math. Monthly 81 (1974), 601–607; corr.: ibid. 82 (1975), 803 Zbl0307.12012MR340214
  2. D. Hilbert, Ein neuer Beweis des Kronecker’schen Fundamentalsatzes über Abel’sche Zahlkörper. Gött. Nachr. (1896), 29–39 Zbl27.0062.03
  3. D. Hilbert, Die Theorie der algebraischen Zahlkörper. Jahresber. DMV 1897, 175–546; Gesammelte Abh. I, 63–363; Engl. Transl. by I. Adamson, Springer-Verlag 1998 
  4. K. Ireland, M. Rosen, A Classical Introduction to Modern Number Theory. Springer Verlag 1982; 2nd ed. 1990 Zbl0482.10001MR1070716
  5. F. Lemmermeyer, Reciprocity Laws. From Euler to Eisenstein. Springer Verlag 2000 Zbl0949.11002MR1761696
  6. D. Marcus, Number Fields. Springer-Verlag 1977 Zbl0383.12001MR457396
  7. A. Speiser, Die Zerlegungsgruppe. J. Reine Angew. Math. 149 (1919), 174–188 
  8. E. Steinbacher, Abelsche Körper als Kreisteilungskörper. J. Reine Angew. Math. 139 (1910), 85–100 
  9. L. Washington, Introduction to Cyclotomic Fields. Springer-Verlag 1982 Zbl0484.12001MR718674

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