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Galois Theory /

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This text offers a clear, efficient exposition of Galois Theory with complete proofs and exercises. Topics include: cubic and quartic formulas; Fundamental Theory of Galois Theory; insolvability of the quintic; Galois's Great Theorem (solvability by radicals of a polynomial is equivalent to sol...

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Bibliographic Details
Main Author: Rotman, Joseph
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint : Springer, 1998.
Edition:Second edition.
Series:Universitext, 0172-5939
Subjects:
Mathematics.
Group theory.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Symmetry
  • Rings
  • Domains and Fields
  • Homomorphisms and Ideals
  • Quotient Rings
  • Polynomial Rings over Fields
  • Prime Ideals and Maximal Ideals
  • Irreducible Polynomials
  • Classical Formulas
  • Splitting Fields
  • The Galois Group
  • Roots of Unity
  • Solvability by Radicals
  • Independence of Characters
  • Galois Extensions
  • The Fundamental Theorem of Galois Theory
  • Applications
  • Galois's Great Theorem
  • Discriminants
  • Galois Groups of Quadratics, Cubics, and Quartics
  • Epilogue
  • Appendix A: Group Theory Dictionary
  • Appendix B: Group Theory Used in the Text
  • Appendix C: Ruler-Compass Constructions
  • Appendix D: Old-fashioned Galois Theory
  • References. Index.