# finite extension

Let $K$ an extension field^{} of $F$. We say that $K$ is a *finite extension ^{}* if
$[K:F]$ is finite. That is, $K$ is a finite dimensional space over $F$.

An important result on finite extensions establishes that any finite extension is also an algebraic extension^{}.

Title | finite extension |

Canonical name | FiniteExtension |

Date of creation | 2013-03-22 11:56:55 |

Last modified on | 2013-03-22 11:56:55 |

Owner | drini (3) |

Last modified by | drini (3) |

Numerical id | 9 |

Author | drini (3) |

Entry type | Definition |

Classification | msc 12F05 |

Synonym | finite field extension |

Related topic | ExtensionField |

Related topic | AlgebraicElement |

Related topic | ExistenceOfTheMinimalPolynomial |

Related topic | AlgebraicExtension |

Related topic | ExtensionMathbbRmathbbQIsNotFinite |

Related topic | AlgebraicSumAndProduct |

Related topic | FiniteExtensionsOfDedekindDomainsAreDedekind |