The Theory of Classical Valuations

Beschreibung

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.
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
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. These are the topics which are the object of this book.

Autor*in

Paulo Ribenboim

Themen in »The Theory of Classical Valuations«

Algebra Division Finite Topology commutative property function fundamental theorem theorem

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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

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