The Theory of Classical Valuations - E-book

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The Theory Of Classical Valuations - ENG

Paulo Ribenboim

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Sinopsis

ISBN:	9781461205517
Formato:	Page Fidelity
Idioma:	Inglés
Editorial:	Springer Nature
Tema:	Matemáticas
Subtema:	Álgebra abstracta
Año de publicación:	2012-12-06

In his studies of cyclotomic fields, in view of establishing his monumental theorem about Fermats 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 Kummers 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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