Galois Theory
The book discusses classical Galois theory in considerable generality, treating fields of characteristic zero and of positive characteristic with consideration of both separable and inseparable extensions, but with a particular emphasis on algebraic exten
- PDF / 1,960,282 Bytes
- 220 Pages / 439.37 x 666.142 pts Page_size
- 10 Downloads / 234 Views
For other titles in this series, go to http://www.springer.com/series/223
Steven H. Weintraub
Galois Theory Second Edition
123
Steven H. Weintraub Department of Mathematics Lehigh University Bethlehem, PA, USA [email protected] Editorial board: Sheldon Axler, San Francisco State University Vincenzo Capasso, Università degli Studi di Milano Carles Casacuberta, Universitat de Barcelona Angus MacIntyre, Queen Mary, University of London Kenneth Ribet, University of California, Berkeley Claude Sabbah, CNRS, École Polytechnique Endre Süli, University of Oxford Wojbor WoyczyĔski, Case Western Reserve University
ISBN: 978-0-387-87574-3 e-ISBN: 978-0-387-87575-0 DOI: 10.1007/978-0-387-87575-0 Library of Congress Control Number: 2008937989 Mathematics Subject Classification (2000): 12-01, 12F10, 11R32 ¤ Springer Science+Business Media, LLC 2006, 2009 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper springer.com
To Judy, after 17 years, and to Blake
Contents
Preface to the First Edition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
Preface to the Second Edition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii 1
Introduction to Galois Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Some Introductory Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 1
2
Field Theory and Galois Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Generalities on Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Extension Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Algebraic Elements and Algebraic Extensions . . . . . . . . . . . . . . 2.5 Splitting Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Extending Isomorphisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Normal, Separable, and Galois Extensions . . . . . . . . . . . . . . . . . 2.8 The Fundamental Theorem of Galois Theory . . . . . . . . . . . . . . . 2.9 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
Data Loading...
