Shortcuts
Top of page (Alt+0)
Page content (Alt+9)
Page menu (Alt+8)
Your browser does not support javascript, some WebOpac functionallity will not be available.
.
Default
.
PageMenu
-
Main Menu
-
Simple Search
.
Advanced Search
.
Journal Search
.
Refine Search Results
.
Preferences
.
Search Menu
Simple Search
.
Advanced Search
.
New Items Search
.
Journal Search
.
Refine Search Results
.
Bottom Menu
Help
Italian
.
English
.
German
.
New Item Menu
New Items Search
.
New Items List
.
Links
SISSA Library
.
ICTP library
.
Italian National web catalog (SBN)
.
Trieste University web catalog
.
Udine University web catalog
.
© LIBERO v6.4.1sp220816
Page content
You are here
:
Catalogue Display
Catalogue Display
The Divisor Class Group of a Krull Domain
.
Bookmark this Record
Catalogue Record 43762
.
.
Author info on Wikipedia
.
.
LibraryThing
.
.
Google Books
.
.
Amazon Books
.
Catalogue Information
Catalogue Record 43762
.
Reviews
Catalogue Record 43762
.
British Library
Resolver for RSN-43762
Google Scholar
Resolver for RSN-43762
WorldCat
Resolver for RSN-43762
Catalogo Nazionale SBN
Resolver for RSN-43762
GoogleBooks
Resolver for RSN-43762
ICTP Library
Resolver for RSN-43762
.
Share Link
Jump to link
Catalogue Information
Field name
Details
Dewey Class
512.44
Title
The Divisor Class Group of a Krull Domain ([EBook] /) / by Robert M. Fossum.
Author
Fossum, Robert M.
Other name(s)
SpringerLink (Online service)
Publication
Berlin, Heidelberg : : Springer Berlin Heidelberg, , 1973.
Physical Details
VIII, 150 p. : online resource.
Series
Ergebnisse der Mathematik und ihrer Grenzgebiete
0071-1136 ; ; 74
ISBN
9783642884054
Summary Note
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.:
Contents note
I. Krull Domains -- § 1. The Definition of a Krull Ring -- § 2. Lattices -- § 3. Completely Integrally Closed Rings -- § 4. Krull’s Normality Criterion and the Mori-Nagata Integral Closure Theorem -- § 5. Divisorial Lattices and the Approximation Theorem -- II. The Divisor Class Group and Factorial Rings -- § 6. The Divisor Class Group and its Functorial Properties -- § 7. Nagata’s Theorem -- § 8. Polynomial Extensions -- § 9. Regular Local Rings -- § 10. Graded Krull Domains and Homogeneous Ideals -- §11. Quadratic Forms -- §12. Murthy’s Theorem -- III. Dedekind Domains -- § 13. Dedekind Domains and a Generalized Approximation Theorem -- § 14. Every Abelian Group is an Ideal Class Group -- § 15. Presentations of Ideal Class Groups of Dedekind Domains -- IV. Descent -- § 16. Galois Descent -- § 17. Radical Descent -- V. Completions and Formal Power Series Extensions -- § 18. The Picard Group -- § 19. Completions, Formal Power Series and Danilov’s Results. -- Appendix I: Terminology and Notation -- Appendix II: List of Results.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-3-642-88405-4
Links to Related Works
Subject References:
Commutative algebra
.
Commutative rings
.
Commutative Rings and Algebras
.
Group theory
.
Group Theory and Generalizations
.
Mathematics
.
Authors:
Fossum, Robert M.
.
Corporate Authors:
SpringerLink (Online service)
.
Series:
Ergebnisse der Mathematik und ihrer Grenzgebiete
.
Classification:
512.44
.
.
ISBD Display
Catalogue Record 43762
.
Tag Display
Catalogue Record 43762
.
Related Works
Catalogue Record 43762
.
Marc XML
Catalogue Record 43762
.
Add Title to Basket
Catalogue Record 43762
.
Catalogue Information 43762
Beginning of record
.
Catalogue Information 43762
Top of page
.
Download Title
Catalogue Record 43762
Export
This Record
As
Labelled Format
Bibliographic Format
ISBD Format
MARC Format
MARC Binary Format
MARCXML Format
User-Defined Format:
Title
Author
Series
Publication Details
Subject
To
File
Email
Reviews
This item has not been rated.
Add a Review and/or Rating
43762
1
43762
-
2
43762
-
3
43762
-
4
43762
-
5
43762
-
Quick Search
Search for