Résumé
In his studies of cyclotomic fields, in view of
establishing his monumental theorem about Fermat's last
theorem, Kummer introduced "local" methods. They are
concerned with divisibility of "ideal numbers" of
cyclotomic fields by lambda = 1 - psi where psi is a
primitive p-th root of 1 (p any odd prime). Henssel
developed Kummer's ideas, constructed the field of p-adic
numbers and proved the fundamental theorem known today.
Kurschak formally introduced the concept of a valuation of
a field, as being real valued functions on the set of
non-zero elements of the field satisfying certain
properties, like the p-adic valuations. Ostrowski, Hasse,
Schmidt and others developed this theory and collectively,
these topics form the primary focus of this book.
Contents
1. Absolute Values of Fields
2. Valuations of a Field
3. Polynomials and Henselian Valued Fields
4. Extensions of Valuations
5. Uniqueness of Extensions of Valuations and Poly-Complete
Fields
6. Numerical relations for valuations with unique
extension
7. Power series and the Structure of Complete Valued
Fields
8. Decomposition and Inertia Theory
9. Ramification Theory
10. Valuation Characterizations of Dedekind Domains
11. Galois Groups of Algebraic Extensions of Infinite
Degree
12. Ideals, Valuations, and Divisors in Algebraic
Extensions of Infinite Degree over Q
13. A Glimpse on Krull Valuations
Bibliography
Appendix on Commutative Fields
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | Springer |
| Auteur(s) | Paulo Ribenboim |
| Parution | 01/02/1999 |
| Nb. de pages | 404 |
| Format | 16 x 24 |
| Couverture | Relié |
| Poids | 691g |
| Intérieur | Noir et Blanc |
| EAN13 | 9780387985251 |
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