Lectures on formally real fields
Author(s)
Bibliographic Information
Lectures on formally real fields
（Lecture notes in mathematics, 1093）
Springer-Verlag, 1984
[2nd ed.]
- : gw
- : us
Available at / 70 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||10938501062S
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science研究室
: gw510/L4972021249315
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Note
"Originally published in 1975 by the Instituto de Matemática Pura e Aplicada, Rio de Janeiro, as volume 22 of the series 'Monografias de matemática'"--Verso t.p
Bibliography: p. [119]-121
Includes index
Description and Table of Contents
Description
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.
Table of Contents
Orderings and semiorderings of fields.- Quadratic forms over formally real fields.- Real algebraic closures.- Some notions from model theory.- The transfer-principle for real closed fields.- The space of orderings and semiorderings.- Real places.- Real henselian fields.- SAP-fields.- Quadratic forms over formally real fields.
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