separable polynomial

Definitions

1. 1

   A polynomial over a given field that has distinct roots in the algebraic closure of said…

   A polynomial over a given field that has distinct roots in the algebraic closure of said field (the number of roots being equal to the degree of the polynomial).

   • Over a perfect field, the separable polynomials are precisely the square-free polynomials.
   • The study of the automorphisms of splitting fields of separable polynomials over a field is referred to as Galois theory.
   • We know that F(#92;zeta) is a normal extension because it is the splitting field of the separable polynomial xⁿ-1 (see Theorem 7.5).

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