Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge

The Divisor Class Group of a Krull Domain

Authors: Fossum, Robert M.

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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 sucĀ­ 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 funcĀ­ 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.

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Buy this book

eBook $99.00 net
( price for USA )
  • ISBN 978-3-642-88405-4
  • digitally watermarked, no DRM
  • included format: PDF
  • eBooks can be used on all Reading Devices
Softcover $129.00 net
( price for USA )
  • ISBN 978-3-642-88407-8
  • free shipping for individuals worldwide
  • usually dispatched within 3 to 5 business days

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Bibliographic Information

Bibliographic Information
Book Title
The Divisor Class Group of a Krull Domain
Series Title
Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge
Series Volume
74
Copyright
1973
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-88405-4
DOI
10.1007/978-3-642-88405-4
Softcover ISBN
978-3-642-88407-8
Edition Number
1
Topics