Field Theory

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


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


Rational Number Cyclic Group Symmetric Group Galois Group Algebraic Closure 
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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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