The Divisor Class Group of a Krull Domain

  • Robert M. Fossum

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 74)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Robert M. Fossum
    Pages 1-5
  3. Robert M. Fossum
    Pages 6-28
  4. Robert M. Fossum
    Pages 29-56
  5. Robert M. Fossum
    Pages 57-81
  6. Robert M. Fossum
    Pages 82-103
  7. Robert M. Fossum
    Pages 104-130
  8. Back Matter
    Pages 131-150

About this book


There are two main purposes for the wntmg of this monograph on factorial rings and the associated theory of the divisor class group of a Krull domain. One is to collect the material which has been published on the subject since Samuel's treatises from the early 1960's. Another is to present some of Claborn's work on Dedekind domains. Since I am not an historian, I tread on thin ice when discussing these matters, but some historical comments are warranted in introducing this material. Krull's work on finite discrete principal orders originating in the early 1930's has had a great influence on ring theory in the suc­ ceeding decades. Mori, Nagata and others worked on the problems Krull suggested. But it seems to me that the theory becomes most useful after the notion of the divisor class group has been made func­ torial, and then related to other functorial concepts, for example, the Picard group. Thus, in treating the group of divisors and the divisor class group, I have tried to explain and exploit the functorial properties of these groups. Perhaps the most striking example of the exploitation of this notion is seen in the works of I. Danilov which appeared in 1968 and 1970.


Abelian group Division Divisorenklassengruppe Factor Finite Krullscher Bereich Lattice approximation class group quadratic form ring theory theorem

Authors and affiliations

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

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1973
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-88407-8
  • Online ISBN 978-3-642-88405-4
  • Series Print ISSN 0071-1136
  • Buy this book on publisher's site