# algebraic conjugates

Let $L$ be an algebraic extension^{} of a field $K$, and let ${\alpha}_{1}\in L$ be algebraic over $K$. Then ${\alpha}_{1}$ is the root of a minimal polynomial^{} $f(x)\in K[x]$. Denote the other roots of $f(x)$ in $L$ by ${\alpha}_{2}$, ${\alpha}_{3},\mathrm{\dots},{\alpha}_{n}$. These (along with ${\alpha}_{1}$ itself) are the *algebraic conjugates* of ${\alpha}_{1}$ 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 polynomial^{}.

Title | algebraic conjugates |
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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 | conjugate^{} |

Related topic | ComplexConjugate |

Related topic | ConjugationMnemonic |