Skip to main content

Galois Theory

  • Chapter
  • 9643 Accesses

Part of the Graduate Texts in Mathematics book series (GTM,volume 242)

Algebra began when quadratic equations were solved by al-Khowarizmi. Its next step was the solution of third and fourth degree equations, published by Cardano in [1545]. Equations of degree 5, however, resisted all efforts at similar solutions, until Abel [1824] and Galois [1830] proved that no such solution exists. Abel’s solution did not hold the germs of future progress, but Galois’s ideas initiated the theory that now bears his name, even though Galois himself lacked a clear definition of fields. The modern version has remained virtually unchanged since Artin’s lectures in the 1920s.

Keywords

  • Galois Group
  • Division Ring
  • Galois Theory
  • Galois Extension
  • General Polynomial

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-0-387-71568-1_5
  • Chapter length: 40 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   54.99
Price excludes VAT (USA)
  • ISBN: 978-0-387-71568-1
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   69.95
Price excludes VAT (USA)
Hardcover Book
USD   69.95
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Rights and permissions

Reprints and Permissions

Copyright information

© 2007 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

(2007). Galois Theory. In: Abstract Algebra. Graduate Texts in Mathematics, vol 242. Springer, New York, NY. https://doi.org/10.1007/978-0-387-71568-1_5

Download citation