Field Theory

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


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 fF[t] such that f(α) = 0, i.e. if α satisfies a polynomial equation
$$ {{\text{a}}_{{\text{n}}}}{\alpha ^{{\text{n}}}} + {\text{ }}...{\text{ }} + {\text{ }}{{\text{a}}_{0}} = {\text{ }}0 $$
with coefficients in F, not all 0. If F is a subfield of E, and every element of E is algebraic over F, we say that E is algebraic over F.


Rational Number Symmetric Group Galois Group Galois Extension Irreducible Polynomial 


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Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

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

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