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Dedekind Domains

  • Robert M. Fossum
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 74)

Abstract

One of the most useful and interesting classes of Krull domains is the class of Dedekind domains. The theory is very familiar. In this chapter of three sections, special properties of Dedekind domains are discussed which are not found in the usual treatments. The first section, in addition to an introductory paragraph or two, contains a generalization of the theorem that a Krull domain with a finite number of prime ideals is a principal ideal domain. The second includes Claborn’s theorem which states that any abelian group is the ideal class group of some Dedekind domain. The third section expands on this result by considering presentations of abelian groups with the intention of showing that the presentation is precisely of the form Div (A)/Prin (A) for a Dedekind domain A.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1973

Authors and Affiliations

  • Robert M. Fossum
    • 1
  1. 1.University of Illinois at Urbana-ChampaignUrbanaUSA

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