separable polynomial

noun1

1. •
   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.