The Divisor Class Group of a Krull Domain:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1973
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete
74 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (VIII, 150 p) |
| ISBN: | 9783642884054 9783642884078 |
| ISSN: | 0071-1136 |
| DOI: | 10.1007/978-3-642-88405-4 |
Internformat
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Datensatz im Suchindex
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| author | Fossum, Robert M. |
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| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-88405-4 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642884054 9783642884078 |
| issn | 0071-1136 |
| language | English |
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| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| spelling | Fossum, Robert M. Verfasser aut The Divisor Class Group of a Krull Domain by Robert M. Fossum Berlin, Heidelberg Springer Berlin Heidelberg 1973 1 Online-Ressource (VIII, 150 p) txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete 74 0071-1136 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 Mathematics Mathematics, general Mathematik Dedekind-Ring (DE-588)4330659-7 gnd rswk-swf Divisorenklasse (DE-588)4150325-9 gnd rswk-swf Krull-Ring (DE-588)4309218-4 gnd rswk-swf Krull-Ring (DE-588)4309218-4 s Divisorenklasse (DE-588)4150325-9 s 1\p DE-604 Dedekind-Ring (DE-588)4330659-7 s 2\p DE-604 https://doi.org/10.1007/978-3-642-88405-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Fossum, Robert M. The Divisor Class Group of a Krull Domain Mathematics Mathematics, general Mathematik Dedekind-Ring (DE-588)4330659-7 gnd Divisorenklasse (DE-588)4150325-9 gnd Krull-Ring (DE-588)4309218-4 gnd |
| subject_GND | (DE-588)4330659-7 (DE-588)4150325-9 (DE-588)4309218-4 |
| title | The Divisor Class Group of a Krull Domain |
| title_auth | The Divisor Class Group of a Krull Domain |
| title_exact_search | The Divisor Class Group of a Krull Domain |
| title_full | The Divisor Class Group of a Krull Domain by Robert M. Fossum |
| title_fullStr | The Divisor Class Group of a Krull Domain by Robert M. Fossum |
| title_full_unstemmed | The Divisor Class Group of a Krull Domain by Robert M. Fossum |
| title_short | The Divisor Class Group of a Krull Domain |
| title_sort | the divisor class group of a krull domain |
| topic | Mathematics Mathematics, general Mathematik Dedekind-Ring (DE-588)4330659-7 gnd Divisorenklasse (DE-588)4150325-9 gnd Krull-Ring (DE-588)4309218-4 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Dedekind-Ring Divisorenklasse Krull-Ring |
| url | https://doi.org/10.1007/978-3-642-88405-4 |
| work_keys_str_mv | AT fossumrobertm thedivisorclassgroupofakrulldomain |