BabelNet

bn:02977392n

Noun Concept

Categories: Field theory, Polynomials

separable polynomial distinct roots inseparable polynomial Separable polynomials

In mathematics, a polynomial P over a given field K is separable if its roots are distinct in an algebraic closure of K, that is, the number of distinct roots is equal to the degree of the polynomial. Wikipedia

Definitions

Examples

Relations

Sources

A polynomial whose number of distinct roots is equal to its degree Wikipedia Disambiguation

Expression whose number of distinct roots is equal to its degree Wikidata

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). Wiktionary

Polynomial that has distinct roots. Wiktionary (translation)

Over a perfect field, the separable polynomials are precisely the square-free polynomials. Wiktionary

The study of the automorphisms of splitting fields of separable polynomials over a field is referred to as Galois theory. Wiktionary

IS A

polynomial

Wikipedia

separable polynomial

Wikidata

separable polynomial

Wiktionary

separable polynomial

Wikipedia Redirections

distinct roots, inseparable polynomial, Separable polynomials