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Algebraic Extensions

  • Juliusz Brzeziński
Chapter
Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Abstract

This chapter describes a kind of field extension most common in Galois theory: algebraic extensions, i.e. extensions K ⊆ L in which each element α ∈ L is a zero of a nontrivial polynomial with coefficients in K. We relate the elements of algebraic extensions to the corresponding polynomials and look at the structures of the simplest extensions K(α) of K. We also introduce the notion of the degree of a field extension and prove some of its properties such as the Tower Law.

References

  1. [C]
    P.M. Cohn, Algebra, vol. 3, Second Edition, John Wiley and Sons, 1991.Google Scholar
  2. [J]
    N. Jacobson, Basic Algebra II, Second Edition, Dover Books on Mathematics (W.H. Freeman and Company), 1989.Google Scholar
  3. [L]
    S. Lang, Algebra, Third Edition, Addison-Wesley, 1993.Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Juliusz Brzeziński
    • 1
    • 2
  1. 1.Department of Mathematical SciencesUniversity of GothenburgGöteborgSweden
  2. 2.Chalmers University of TechnologyGöteborgSweden

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