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Über Die Klassenzahl Abelscher Zahlkörper by Helmut Hasse, J. Martinet

Über Die Klassenzahl Abelscher Zahlkörper

by Helmut Hasse , J. Martinet
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Book cover type: Paperback
  • ISBN13: 9783642698873
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 190
  • Original Price: EUR 51.39
  • Language: German
  • Edition: Softcover Repri
  • Item Weight: 359 grams
  • BISAC Subject(s): Number Theory

Die a1gebraische Zahlentheorie hat sich aus den ersten Ansatzen bei G a 11 Il unter den Hinden der groBen Meister des vergangenen und dieses Jahrhunderts zu einem gewaltigen Lehrgebaude entwickelt, das heute iiberreich an allgemeinen Satzen, beherrsohenden methodischen Gesichtspunkten und tiefen strukturellen Einsichten im wesentlichen abgeschlossen dasteht. Die erste Phase dieser Ent- wicklung hat Hilbert [2] in seinem beriihmten Bericht iiber die Theorie der alge- bra. ischen Zahlkorperl) zusammenfassend dargestellt. Dieser Bericht bringt in seinen . ersten beiden Teilen die allgemeinen Grundlagen der Theorie und geht dann in weiteren drei Teilen auf drei spezielle Typen algebraischer Zahlkorper des naheren ein, namlich auf die quadratischen Zahlkorper, die Kreiskorper und die Kummerschen Zahlkorper. Vom heutigen Standpunkt aUi! gesehen fiihren diese letzten drei Teile des Hilbertschen Zahlberichts Spezialfalle del- allgemeinen Theorie der relativ-abelschen Zahlkorper durcb. Sie leiten die zweite Phase der Entwicklung ein, zu der Hilbert selbst mit seiner kiihnen Konzeption des KlassenkorperbegrifJs und der Hauptsatze der Klassenkorpertheorie den Anstoll gab. Diese zweite Phase, die Theorie der relativ-abelschen Zahlkorper, in der die Klassenkorpertheorie in voller Allgemeinheit entwickelt und auf die Herleitung des allgemeinsten Reziprozitatsgesetzes angewandt wird, habe ich [1] im AnschluB an l Hilberts Zablbericbt in einem dreiteiligen Bericht ) zusammenfassend dargestellt. Bei dieser ganzen Entwicklung, die von allgemeinen theoretischen, struktu- rellen, methodischen und systematischen Gesichtspunkten geleitet wurde, ist nun aber das jedem echten Zahlentheoretiker eigene Bediirfnis nach expliziter Be- heuschung des behandelten Gegenstandes bis zur Durchfiibrung numerischer Bei- spiele stark in den Hintergrund getreten.

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