Last Updated
：2025/12/04
algebraically independent
Adjective
not-comparable
Japanese Meaning
ある体拡大 L/K において、拡大体 L の部分集合 S の各元が、基底体 K の係数を持つ任意の非自明な多項式方程式（すなわち、定数項だけでなく変数も含む多項式）の解にならないこと、すなわち、その元同士に対して代数的な依存関係が存在しない状態を指す。
Quizzes for review
(algebra, field theory) (Of a subset S of the extension field L of a given field extension L / K) whose elements do not satisfy any non-trivial polynomial equation with coefficients in K.
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algebraically independent
The elements α, β, and γ are algebraically independent over the base field, so any polynomial relation among them with coefficients in the base field must be trivial.
See correct answer
The elements α, β, and γ are algebraically independent over the base field, so any polynomial relation among them with coefficients in the base field must be trivial.
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