Separable Polynomial Definition

noun

(algebra SEPARABLE 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 .
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