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Springer Monographs in Mathematics

The Theory of Classical Valuations

Authors: Ribenboim, Paulo

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eBook 130,89 €
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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.

Reviews

"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)

Buy this book

eBook 130,89 €
price for Spain (gross)
  • ISBN 978-1-4612-0551-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 171,59 €
price for Spain (gross)
  • ISBN 978-0-387-98525-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 171,59 €
price for Spain (gross)
  • ISBN 978-1-4612-6814-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
The Theory of Classical Valuations
Authors
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