2. Polynomials and Field Theory

  1. Stephen C. Newman

Published Online: 23 MAY 2012

DOI: 10.1002/9781118336816.ch2

A Classical Introduction to Galois Theory

A Classical Introduction to Galois Theory

How to Cite

Newman, S. C. (2012) Polynomials and Field Theory, in A Classical Introduction to Galois Theory, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118336816.ch2

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:

  • polynomials and field theory, and fields needed;
  • Division and Euclidean Algorithms, of ambient fields;
  • algebraic extensions, degree of extensions and derivatives;
  • isomorphism extension on arbitrary, polynomials and splitting field

Summary

This chapter contains sections titled:

  • Divisibility

  • Algebraic Extensions

  • Degree of Extensions

  • Derivatives

  • Primitive Element Theorem

  • Isomorphism Extension Theorem and Splitting Fields