English Dictionary

separable polynomial

名詞

(algebra, field theory) 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).

日本語の意味

与えられた体の代数的閉体において、重複する根を持たず、すべての根が単純である多項式。つまり、多項式の次数と根の個数が一致するもの。

To determine whether the field extension is Galois, we first check if the minimal polynomial is a separable polynomial over the base field.

体拡大がガロア拡大であるかを判定するために、まず既約多項式が基底体上で重根を持たない多項式（分離多項式）であるかを確認します。

意味（1）

(algebra, field theory) 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.

separable polynomials （ plural ）