# normal closure

Let $K$ be an extension field^{} of $F$. A normal closure^{} of $K/F$ is a field $L\supseteq K$ that is a normal extension^{} of $F$ and is minimal^{} in that respect, i.e. no proper subfield of $L$ containing $K$ is normal over $F$. If $K$ is an algebraic extension^{} of $F$, then a normal closure for $K/F$ exists and is unique up to isomorphism^{}.

Title | normal closure |
---|---|

Canonical name | NormalClosure |

Date of creation | 2013-03-22 13:09:36 |

Last modified on | 2013-03-22 13:09:36 |

Owner | scanez (1021) |

Last modified by | scanez (1021) |

Numerical id | 5 |

Author | scanez (1021) |

Entry type | Definition |

Classification | msc 12F10 |