The Theory of Classical Valuations / Edition 1

The Theory of Classical Valuations / Edition 1

by Paulo Ribenboim, P. Ribenboim, Paulo Ribenhoim
     
 

ISBN-10: 0387985255

ISBN-13: 9780387985251

Pub. Date: 05/21/1999

Publisher: Springer New York

Valuation theory is used constantly in algebraic number theory and field theory, and is currently gaining considerable research interest. Ribenboim fills a unique niche in the literature as he presents one of the first introductions to classical valuation theory in this up-to-date rendering of the authors long-standing experience with the applications of the theory

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Overview

Valuation theory is used constantly in algebraic number theory and field theory, and is currently gaining considerable research interest. Ribenboim fills a unique niche in the literature as he presents one of the first introductions to classical valuation theory in this up-to-date rendering of the authors long-standing experience with the applications of the theory. The presentation is fully up-to-date and will serve as a valuable resource for students and mathematicians.

Product Details

ISBN-13:
9780387985251
Publisher:
Springer New York
Publication date:
05/21/1999
Series:
Springer Monographs in Mathematics Series
Edition description:
1999
Pages:
403
Product dimensions:
6.14(w) x 9.21(h) x 1.00(d)

Table of Contents

Preface
Notations
Introduction1
Ch. 1Absolute Values of Fields3
Ch. 2Valuations of a Field55
Ch. 3Polynomials and Henselian Valued Fields79
Ch. 4Extensions of Valuations107
Ch. 5Uniqueness of Extensions of Valuations and Poly-Complete Fields127
Ch. 6Extensions of Valuations: Numerical Relations151
Ch. 7Power Series and the Structure of Complete Valued Fields185
Ch. 8Decomposition and Inertia Theory213
Ch. 9Ramification Theory227
Ch. 10Valuation Characterizations of Dedekind Domains263
Ch. 11Galois Groups of Algebraic Extensions of Infinite Degree307
Ch. 12Ideals, Valuations, and Divisors in Algebraic Extensions of Infinite Degree over Q333
Ch. 13A Glimpse of Krull Valuations365
AppCommutative Fields and Characters of Finite Abelian Groups373
Bibliography391
Index395

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