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Table of contents (10 chapters)
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Front Matter
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Back Matter
About this book
Absolute values and their completions - like the p-adic number fields- play an important role in number theory. Krull's generalization of absolute values to valuations made applications in other branches of mathematics, such as algebraic geometry, possible. In valuation theory, the notion of a completion has to be replaced by that of the so-called Henselization.
In this book, the theory of valuations as well as of Henselizations is developed. The presentation is based on the knowledge aquired in a standard graduate course in algebra. The last chapter presents three applications of the general theory -as to Artin's Conjecture on the p-adic number fields- that could not be obtained by the use of absolute values only.
Bibliographic Information
Book Title: Lectures on Formally Real Fields
Authors: Alexander Prestel
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0101548
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1984
Softcover ISBN: 978-3-540-13885-3Published: 01 November 1984
eBook ISBN: 978-3-540-39093-0Published: 05 January 2007
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XI, 128
Additional Information: Originally published by the Instituto de Matematica Pura e Aplicada, Rio de Janeiro