# degree of an algebraic number

Let $\alpha $ be an algebraic number^{}. The *degree* of $\alpha $ is the degree (http://planetmath.org/Degree8) of the minimal polynomial^{} for $\alpha $ over $\mathbb{Q}$.

In a manner to polynomials^{}, the degree of $\alpha $ may be denoted $\mathrm{deg}\alpha $.

For example, since ${x}^{3}-2$ is the minimal polynomial for $\sqrt[3]{2}$ over $\mathbb{Q}$, we have $\mathrm{deg}\sqrt[3]{2}=3$.

Title | degree of an algebraic number |

Canonical name | DegreeOfAnAlgebraicNumber |

Date of creation | 2013-03-22 17:50:05 |

Last modified on | 2013-03-22 17:50:05 |

Owner | Wkbj79 (1863) |

Last modified by | Wkbj79 (1863) |

Numerical id | 4 |

Author | Wkbj79 (1863) |

Entry type | Definition |

Classification | msc 12E05 |

Classification | msc 12F05 |

Classification | msc 11C08 |

Classification | msc 11R04 |

Related topic | AlgebraicNumber |

Related topic | Degree8 |

Related topic | MinimalPolynomial |

Related topic | TheoryOfAlgebraicNumbers |