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单词 AlgebraicConjugates
释义

algebraic conjugates


Let L be an algebraic extensionMathworldPlanetmath of a field K, and let α1L be algebraic over K. Then α1 is the root of a minimal polynomialPlanetmathPlanetmath f(x)K[x]. Denote the other roots of f(x) in L by α2, α3,,αn. These (along with α1 itself) are the algebraic conjugates of α1 and any two are said to be algebraically conjugate.

The notion of algebraic conjugacy is a special case of group conjugacy in the case where the group in question is the Galois group of the above minimal polynomial, viewed as acting on the roots of said polynomialPlanetmathPlanetmath.

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更新时间:2025/5/4 11:41:48