The Divisor Class Group of a Krull Domain

Robert M. Fossum

ISBN 10: 3642884075 / ISBN 13: 9783642884078

Edité par Springer Berlin Heidelberg, Springer Berlin Heidelberg Apr 2012, 2012

A propos de cet article

Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 160 pp. Englisch.

N° de réf. du vendeur 9783642884078

Détails bibliographiques

• Titre: The Divisor Class Group of a Krull Domain
• Éditeur: Springer Berlin Heidelberg, Springer Berlin Heidelberg Apr 2012
• Date de parution: 2012
• Langue: anglais
• ISBN à 10 chiffres: 3642884075
• ISBN à 13 chiffres: 9783642884078
• Reliure: Taschenbuch
• État de l'article: Neu
• Dimensions: 235 L x 155 H x 9 P (en millimètres) 235 millimètres de largeur par 155 millimètres de hauteur par 9 millimètres de profondeur
• Poids: 254 grammes

A propos de ce titre

Synopsis

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.