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Galois Theory

  • Joseph Rotman

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Joseph Rotman
    Pages 1-7
  3. Joseph Rotman
    Pages 7-13
  4. Joseph Rotman
    Pages 13-17
  5. Joseph Rotman
    Pages 17-21
  6. Joseph Rotman
    Pages 21-23
  7. Joseph Rotman
    Pages 24-31
  8. Joseph Rotman
    Pages 31-38
  9. Joseph Rotman
    Pages 38-43
  10. Joseph Rotman
    Pages 44-49
  11. Joseph Rotman
    Pages 50-58
  12. Joseph Rotman
    Pages 59-63
  13. Joseph Rotman
    Pages 63-70
  14. Joseph Rotman
    Pages 71-75
  15. Joseph Rotman
    Pages 76-79
  16. Joseph Rotman
    Pages 79-82
  17. Joseph Rotman
    Pages 83-85
  18. Joseph Rotman
    Pages 85-90
  19. Joseph Rotman
    Pages 90-95
  20. Joseph Rotman
    Pages 95-100
  21. Back Matter
    Pages 107-158

About this book

Introduction

The first edition aimed to give a geodesic path to the Fundamental Theorem of Galois Theory, and I still think its brevity is valuable. Alas, the book is now a bit longer, but I feel that the changes are worthwhile. I began by rewriting almost all the text, trying to make proofs clearer, and often giving more details than before. Since many students find the road to the Fundamental Theorem an intricate one, the book now begins with a short section on symmetry groups of polygons in the plane; an analogy of polygons and their symmetry groups with polynomials and their Galois groups can serve as a guide by helping readers organize the various definitions and constructions. The exposition has been reorganized so that the discussion of solvability by radicals now appears later; this makes the proof of the Abel-Ruffini theo rem easier to digest. I have also included several theorems not in the first edition. For example, the Casus Irreducibilis is now proved, in keeping with a historical interest lurking in these pages.

Keywords

Galois group Galois theory Group theory Symmetry group field homomorphism

Authors and affiliations

  • Joseph Rotman
    • 1
  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0617-0
  • Copyright Information Springer-Verlag New York, Inc. 1998
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-98541-1
  • Online ISBN 978-1-4612-0617-0
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site