# corollary to the compositum of a Galois extension and another extension is Galois

###### Corollary 1.

Let $E\mathrm{/}K$ be a Galois extension^{} of fields, let $F\mathrm{/}K$ be an arbitrary extension and assume that $E$ and $F$ are both subfields^{} of some other larger field $T$. The compositum of $E$ and $F$ is here denoted by $E\mathit{}F$. Then $\mathrm{[}EF\mathrm{:}F\mathrm{]}\mathrm{=}\mathrm{[}E\mathrm{:}E\mathrm{\cap}F\mathrm{]}$.

This follows immediately from item (2) of the theorem.

Title | corollary to the compositum of a Galois extension and another extension is Galois |
---|---|

Canonical name | CorollaryToTheCompositumOfAGaloisExtensionAndAnotherExtensionIsGalois |

Date of creation | 2013-03-22 18:42:04 |

Last modified on | 2013-03-22 18:42:04 |

Owner | rm50 (10146) |

Last modified by | rm50 (10146) |

Numerical id | 4 |

Author | rm50 (10146) |

Entry type | Corollary |

Classification | msc 12F99 |

Classification | msc 11R32 |