The Divisor Class Group of a Krull Domain

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 presen...

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Main Author: Fossum, Robert M.
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1973, 1973
Edition:1st ed. 1973
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics
Subjects:
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Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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