Advertisement

Galois’s Great Theorem

  • Joseph Rotman
Part of the Universitext book series (UTX)

Abstract

We prove the converse of Theorem 74: Solvability of the Galois group of f(x) ∈F[x], where F is a field of characteristic 0, implies f(x) is solvable by radicals. We begin with some lemmas; the first one has a quaint name signifying its use as a device to get around the possible absence of roots of unity in the ground field.

Keywords

Galois Group Solvable Group GALOIS Theory Galois Extension Radical Extension 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 16.
    E. Houston, A Linear Algebra Approach to Cyclic Extensions in Galois Theory, Amer. Math. Monthly 100 (1993), 64–66.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

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

Personalised recommendations