# radical extension

A radical tower is a field extension $L/F$ which has a filtration^{}

$$F={L}_{0}\subset {L}_{1}\subset \mathrm{\cdots}\subset {L}_{n}=L$$ |

where for each $i$, $$, there exists an element ${\alpha}_{i}\in {L}_{i+1}$ and a natural number^{} ${n}_{i}$ such that ${L}_{i+1}={L}_{i}({\alpha}_{i})$ and ${\alpha}_{i}^{{n}_{i}}\in {L}_{i}$.

A radical extension is a field extension $K/F$ for which there exists a radical tower $L/F$ with $L\supset K$. The notion of radical extension coincides with the informal concept of solving for the roots of a polynomial^{} by radicals^{}, in the sense that a polynomial over $K$ is solvable by radicals if and only if its splitting field^{} is a radical extension of $F$.

Title | radical extension |
---|---|

Canonical name | RadicalExtension |

Date of creation | 2013-03-22 12:08:35 |

Last modified on | 2013-03-22 12:08:35 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 7 |

Author | djao (24) |

Entry type | Definition |

Classification | msc 12F10 |

Synonym | radical tower |