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The Divisor Class Group of a Krull Domain

  • Book
  • © 1973

Overview

Authors:
  1. Robert M. Fossum

    1. University of Illinois at Urbana-Champaign, Urbana, USA

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Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge (MATHE2, volume 74)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Introduction

    • Robert M. Fossum
    Pages 1-5

  3. Krull Domains

    • Robert M. Fossum
    Pages 6-28

  4. The Divisor Class Group and Factorial Rings

    • Robert M. Fossum
    Pages 29-56

  5. Dedekind Domains

    • Robert M. Fossum
    Pages 57-81

  6. Descent

    • Robert M. Fossum
    Pages 82-103

  7. Completions and Formal Power Series Extensions

    • Robert M. Fossum
    Pages 104-130

  8. Back Matter

    Pages 131-150
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Keywords

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.

Authors and Affiliations

  • University of Illinois at Urbana-Champaign, Urbana, USA

    Robert M. Fossum

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