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Field Theory

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

Abstract

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.

Keywords

Rational Number Symmetric Group Galois Group Galois Extension Irreducible Polynomial 
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-Verlag New York Inc. 1987

Authors and Affiliations

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

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