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单词 AlgebraicallyDependent
释义

algebraically dependent


Let L be a field extension of a field K. Two elements α,β of L are algebraically dependent if there exists a non-zero polynomialPlanetmathPlanetmath f(x,y)K[x,y] such that f(α,β)=0. If no such polynomial exists, α and β are said to be algebraically independent.

More generally, elements α1,,αnL are said to be algebraically dependent if there exists a non-zero polynomial f(x1,,xn)K[x1,,xn] such that f(α1,α2,,αn)=0. If no such polynomial exists, the collectionMathworldPlanetmath of α’s are said to be algebraically independent.

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更新时间:2025/5/4 12:36:41