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    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
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The Divisor Class Group of a Krull Domain

The Divisor Class Group of a Krull Domain

Fossum, Robert M.

Paperback

Series: Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge, Book 74

Algebra

ISBN10: 3642884075
ISBN13: 9783642884078
Publisher: Springer Nature
Published: Apr 10 2012
Pages: 150
Weight: 0.51
Height: 0.34 Width: 6.14 Depth: 9.21
Language: English
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.

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