Author | Fossum, Robert M. author |
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Title | The Divisor Class Group of a Krull Domain [electronic resource] / by Robert M. Fossum |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1973 |
Connect to | http://dx.doi.org/10.1007/978-3-642-88405-4 |
Descript | VIII, 150 p. online resource |
I. Krull Domains -- ยง 1. The Definition of a Krull Ring -- ยง 2. Lattices -- ยง 3. Completely Integrally Closed Rings -- ยง 4. Krullโs Normality Criterion and the Mori-Nagata Integral Closure Theorem -- ยง 5. Divisorial Lattices and the Approximation Theorem -- II. The Divisor Class Group and Factorial Rings -- ยง 6. The Divisor Class Group and its Functorial Properties -- ยง 7. Nagataโs Theorem -- ยง 8. Polynomial Extensions -- ยง 9. Regular Local Rings -- ยง 10. Graded Krull Domains and Homogeneous Ideals -- ยง11. Quadratic Forms -- ยง12. Murthyโs Theorem -- III. Dedekind Domains -- ยง 13. Dedekind Domains and a Generalized Approximation Theorem -- ยง 14. Every Abelian Group is an Ideal Class Group -- ยง 15. Presentations of Ideal Class Groups of Dedekind Domains -- IV. Descent -- ยง 16. Galois Descent -- ยง 17. Radical Descent -- V. Completions and Formal Power Series Extensions -- ยง 18. The Picard Group -- ยง 19. Completions, Formal Power Series and Danilovโs Results. -- Appendix I: Terminology and Notation -- Appendix II: List of Results