# normal extension

A field extension $K/F$ is *normal* if every irreducible polynomial^{} $f\in F[x]$ which has at least one root in $K$ splits (factors into a product^{} of linear factors) in $K[x]$.

An extension^{} $K/F$ of finite degree is normal if and only if there exists a polynomial^{} $p\in F[x]$ such that $K$ is the splitting field^{} for $p$ over $F$.

Title | normal extension^{} |
---|---|

Canonical name | NormalExtension |

Date of creation | 2013-03-22 12:08:15 |

Last modified on | 2013-03-22 12:08:15 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 10 |

Author | djao (24) |

Entry type | Definition |

Classification | msc 12F10 |

Synonym | normal |

Related topic | SplittingField |