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- About this book
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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.
- Reviews
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"It is well written, encyclopedic, and authoritative and probably belongs on the shelf of any commutative algebraist or algebraic number theorist."--MATHEMATICAL REVIEWS
- Table of contents (14 chapters)
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Introduction
Pages 1-1
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Absolute Values of Fields
Pages 3-54
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Valuations of a Field
Pages 55-78
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Polynomials and Henselian Valued Fields
Pages 79-105
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Extensions of Valuations
Pages 107-125
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Table of contents (14 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- The Theory of Classical Valuations
- Authors
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- Paulo Ribenboim
- Series Title
- Springer Monographs in Mathematics
- Copyright
- 1999
- Publisher
- Springer-Verlag New York
- Copyright Holder
- Springer Science+Business Media New York
- eBook ISBN
- 978-1-4612-0551-7
- DOI
- 10.1007/978-1-4612-0551-7
- Hardcover ISBN
- 978-0-387-98525-1
- Softcover ISBN
- 978-1-4612-6814-7
- Series ISSN
- 1439-7382
- Edition Number
- 1
- Number of Pages
- XI, 403
- Topics
