# cyclotomic extension

###### Definition.

Let $K$ be a field and let $\overline{K}$ be a fixed algebraic closure^{} of $K$. A cyclotomic extension of $K$ is an extension field^{} of the form $K\mathit{}\mathrm{(}\zeta \mathrm{)}$ where $\zeta \mathrm{\in}\overline{K}$ is a root of unity^{}.

Title | cyclotomic extension |
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Canonical name | CyclotomicExtension |

Date of creation | 2013-03-22 15:05:17 |

Last modified on | 2013-03-22 15:05:17 |

Owner | alozano (2414) |

Last modified by | alozano (2414) |

Numerical id | 4 |

Author | alozano (2414) |

Entry type | Definition |

Classification | msc 11-00 |

Classification | msc 11R18 |

Related topic | KroneckerWeberTheorem |

Related topic | CyclotomicField |