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.

Title algebraic conjugates
Canonical name AlgebraicConjugates
Date of creation 2013-03-22 13:58:39
Last modified on 2013-03-22 13:58:39
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 9
Author mathcam (2727)
Entry type Definition
Classification msc 11R04
Synonym algebraically conjugate
Synonym conjugatePlanetmathPlanetmath
Related topic ComplexConjugate
Related topic ConjugationMnemonic