Overview
- Area of great interest where there is no book to serve as a first introduction to the topic * Fully up-to-date as the author draws upon his long-standing experience * Ribenboim has written other successful Springer titles * Fills a niche in the literature and will serve as the ultimate resource on the subject
Part of the book series: Springer Monographs in Mathematics (SMM)
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About this book
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.
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Table of contents (14 chapters)
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Front Matter
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Back Matter
Reviews
"It is well written, encyclopedic, and authoritative and probably belongs on the shelf of any commutative algebraist or algebraic number theorist."--MATHEMATICAL REVIEWS
Authors and Affiliations
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Bibliographic Information
Book Title: The Theory of Classical Valuations
Authors: Paulo Ribenboim
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-1-4612-0551-7
Publisher: Springer New York, NY
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 1999
Hardcover ISBN: 978-0-387-98525-1Published: 21 May 1999
Softcover ISBN: 978-1-4612-6814-7Published: 04 October 2012
eBook ISBN: 978-1-4612-0551-7Published: 06 December 2012
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XI, 403
Topics: K-Theory