The Divisor Class Group of a Krull Domain

Springer-Verlag

1973

150 p.

Ergebnisse der Mathematik und ihrer Grenzgebiete ; Bd 2, Heft 74

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.

Английский