Last Updated：2025/12/04

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(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).

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separable polynomial

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Source Word

separable polynomial

Noun

(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).

Japanese Meaning

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。

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Google Translation / DeepL Translation

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。

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Sense（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).