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.
| ISBN: | 9780387985251 |
| Publication date: | 1st June 1999 |
| Author: | Paulo Ribenboim |
| Publisher: | Springer an imprint of Springer New York |
| Format: | Hardback |
| Pagination: | 403 pages |
| Series: | Springer Monographs in Mathematics |
| Genres: |
Algebraic topology |
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.
The Theory of Classical Valuations features in the following genres: Algebraic topology
The Theory of Classical Valuations is available in Paperback, Hardback
The Theory of Classical Valuations was written by Paulo Ribenboim and published by Springer an imprint of Springer New York
The Theory of Classical Valuations has 403 pages
Yes it is part of Springer Monographs in Mathematics series