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Galois Theory

  • Textbook
  • © 1998

Overview

Authors:
  1. Joseph Rotman

    1. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, USA

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Part of the book series: Universitext (UTX)

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Table of contents (20 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Symmetry

    • Joseph Rotman
    Pages 1-7

  3. Rings

    • Joseph Rotman
    Pages 7-13

  4. Domains and Fields

    • Joseph Rotman
    Pages 13-17

  5. Homomorphisms and Ideals

    • Joseph Rotman
    Pages 17-21

  6. Quotient Rings

    • Joseph Rotman
    Pages 21-23

  7. Polynomial Rings over Fields

    • Joseph Rotman
    Pages 24-31

  8. Prime Ideals and Maximal Ideals

    • Joseph Rotman
    Pages 31-38

  9. Irreducible Polynomials

    • Joseph Rotman
    Pages 38-43

  10. Classical Formulas

    • Joseph Rotman
    Pages 44-49

  11. Splitting Fields

    • Joseph Rotman
    Pages 50-58

  12. The Galois Group

    • Joseph Rotman
    Pages 59-63

  13. Roots of Unity

    • Joseph Rotman
    Pages 63-70

  14. Solvability by Radicals

    • Joseph Rotman
    Pages 71-75

  15. Independence of Characters

    • Joseph Rotman
    Pages 76-79

  16. Galois Extensions

    • Joseph Rotman
    Pages 79-82

  17. The Fundamental Theorem of Galois Theory

    • Joseph Rotman
    Pages 83-85

  18. Applications

    • Joseph Rotman
    Pages 85-90

  19. Galois’s Great Theorem

    • Joseph Rotman
    Pages 90-95

  20. Discriminants

    • Joseph Rotman
    Pages 95-100
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, USA

    Joseph Rotman

Bibliographic Information

  • Book Title: Galois Theory

  • Authors: Joseph Rotman

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-1-4612-0617-0

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1998

  • Softcover ISBN: 978-0-387-98541-1Published: 01 October 1998

  • eBook ISBN: 978-1-4612-0617-0Published: 06 December 2012

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 2

  • Number of Pages: XIV, 176

  • Topics: Group Theory and Generalizations

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