6. Radical Extensions and Solvability by Radicals

  1. Stephen C. Newman

Published Online: 23 MAY 2012

DOI: 10.1002/9781118336816.ch6

A Classical Introduction to Galois Theory

A Classical Introduction to Galois Theory

How to Cite

Newman, S. C. (2012) Radical Extensions and Solvability by Radicals, in A Classical Introduction to Galois Theory, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118336816.ch6

Author Information

  1. University of Alberta, Edmonton, Alberta, Canada

Publication History

  1. Published Online: 23 MAY 2012
  2. Published Print: 13 JUL 2012

ISBN Information

Print ISBN: 9781118091395

Online ISBN: 9781118336816

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Keywords:

  • radical extensions and solvability by radicals;
  • irreducible polynomials of prime degree, and unique properties;
  • solvability by irreducible radicals, and irreducible radical extensions;
  • Gauss's theorem on cyclotomic polynomials

Summary

This chapter contains sections titled:

  • Basic Results on Radical Extensions

  • Gauss's Theorem on Cyclotomic Polynomials

  • Abel's Theorem on Radical Extensions

  • Polynomials of Prime Degree