Last Updated
：2025/12/04
separable polynomial
Noun
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。
（ plural ）
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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
To determine whether the field extension is Galois, we first check if the minimal polynomial is a separable polynomial over the base field.
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To determine whether the field extension is Galois, we first check if the minimal polynomial is a separable polynomial over the base field.
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