Field Theory

  • Serge Lang
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

Let F be a subfield of a field E. We also say that E is an extension of F and we denote the extension by E/F. Let F be a field. An element α in some extension of F is said to be algebraic over F if there exists a non-zero polynomial f ∈ F[t]such that f(α) = 0, i.e. if α satisfies a polynomial equation

Keywords

Rational Number Cyclic Group Symmetric Group Galois Group Algebraic Closure 
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.

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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Serge Lang
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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