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Lectures on Formally Real Fields A. Prestel

Lectures on Formally Real Fields

A. Prestel

Published November 1st 1984
ISBN : 9783540138853
Paperback
128 pages
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 About the Book 

Absolute values and their completions - like the p-adic number fields- play an important role in number theory. Krulls generalization of absolute values to valuations made applications in other branches of mathematics, such as algebraic geometry,MoreAbsolute values and their completions - like the p-adic number fields- play an important role in number theory. Krulls 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 Artins Conjecture on the p-adic number fields- that could not be obtained by the use of absolute values only.