Lectures on Formally Real Fields
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, possibl
- PDF / 5,514,719 Bytes
- 134 Pages / 468 x 684 pts Page_size
- 79 Downloads / 247 Views
1093 Alexander Prestel
Lectures on Formally Real Fields
Springer-Verlag Berlin Heidelberg New York Tokyo 1984
Lecture Notes in Mathematics Edited by A. Oold and B. Eckmann Subseries: Instituto de Maternatica Pura e Aplicada, Rio de Janeiro Adviser: C. Camacho
1093 Alexander Prestel
Lectures on Formally Real Fields
Springer-Verlag Berlin Heidelberg New York Tokyo 1984
Author
Alexander Prestel Fakultat tur Mathematik, Universitat Konstanz Postfach 5560, 7750 Konstanz, Federal Republic of Germany
This book was originally published in 1975 by the Instituto de Maternatica Pura e Aplicada, Rio de Janeiro as volume 22 of the series "Monografias de Matematica".
AMS Subject Classification (1980): 12015, lOC04 ISBN 3-540-13885-4 Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-13885-4 Springer-Verlag New York Heidelberg Berlin Tokyo This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich.
© by Springer-Verlag Berlin Heidelberg 1984 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach I Bergstr. 2146/3140-543210
To
the memory of my parents
Preface Ten years ago, in 1974, these lectures were given at the 'Instituto de Matematica Pura e Aplicada', in Rio de Janeiro. In 1975 the notes of these lectures appeared in the series 'Monografias de Matematica' as No.22 published by IMPA. From that time on the notes served as an introductory text for the theory of real fields and its connections with valuation theory and quadratic form theory. Since the 'Lectures on formally real fields' have been used in many publications as a standard reference and since currently they still seem to be the only introductory text to this theory, I gratefully accepted the proposal of C. Camacho to republish them in the IMPA-Subseries of the 'Lecture Notes in Mathematics'. It seems wise not to make chang8s in this new edition apart from correcting misprints and a few minor errors: The only change made is to replace the term q-ordering by semiordering, since the latter term turned out to be
almost exclusively used in the recent literature. For the developments during the last decade in this theory, particularly in the theory of reduced quadratic forms, I would like to refer the reader to two publications of T.Y. Lam: his survey article The Theory of Ordered Fields
[in Ring Theory and Algebra III
(ed. B.
Mc Donald), Lecture Notes in Pure and Applied Math., Vol. 55, Dekker, New York, 1980, p. 1-152] and to his expository notes Orderings, Valuations and Quadratic Forms
[Conf. Board of the Math.
Sciences, Regional Conf. Series in Math., No. 52, Providence,R.I.,1983]. Finally I would like to thank Edda Polte for preparing the typescript of th
Data Loading...
