algebraically independent

not-comparable

(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.

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。

What is this buttons?

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.

Google Translation / DeepL Translation

α、β、γは基底体上で代数的に独立しているため、基底体の係数によるそれらの間の任意の多項式関係は自明（零多項式）でなければならない。

Details

Sense（1）

(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.

Details

algebraically independent

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