separable polynomial
separable polynomial · separable polynomials
A polynomial over a given field that has distinct roots in the algebraic closure of…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).
Meaning
1 sensesA 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.
Translations
3 languagesForms
plural: separable polynomials| Singular | separable polynomial |
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| Plural | separable polynomials |
regular