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Discriminants

  • Joseph Rotman
Part of the Universitext book series (UTX)

Abstract

Let F be a field of characteristic 0, let f(x) ∈ F[x] be a polynomial of degree n having splitting field E/F, and let G = Gal(E/F). If α1,..., α n are the roots of f(x) in E (with repeated roots, if any, occurring several times), define
$$ \Delta = \prod\limits_{{i < j}} {\left( {{\alpha_i} - {\alpha_j}} \right)} $$
. The number Δ depends on the indexing of the roots; a new indexing may change the sign of Δ. Therefore D2 depends only on the set of roots.

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Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • Joseph Rotman
    • 1
  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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