Reference : The degree of Kummer extensions of number fields |

E-prints/Working papers : First made available on ORBilu | |||

Physical, chemical, mathematical & earth Sciences : Mathematics | |||

http://hdl.handle.net/10993/42470 | |||

The degree of Kummer extensions of number fields | |

English | |

Perucca, Antonella [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |

Sgobba, Pietro [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |

Tronto, Sebastiano [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |

Undated | |

No | |

[en] number field ; Kummer theory ; degree ; Kummer extension | |

[en] Let K be a number field, and let \alpha_1, ... , \alpha_r be elements of K* which generate a subgroup of K* of rank r. Consider the cyclotomic-Kummer extensions of K given by K(\zeta_n, \sqrt[n_1]{\alpha_1}, ... , \sqrt[n_r]{\alpha_r}), where n_i divides n for all i. There is an integer x such that these extensions have maximal degree over K(\zeta_g, \sqrt[g_1]{\alpha_1}, ... , \sqrt[g_r]{\alpha_r}), where g=\gcd(n,x) and g_i=\gcd(n_i,x). We prove that the constant x is computable. This result reduces to finitely many cases the computation of the degrees of the extensions K(\zeta_{n}, \sqrt[{n_1}]{\alpha_1}, ... , \sqrt[{n_r}]{\alpha_r}) over K. | |

Researchers | |

http://hdl.handle.net/10993/42470 |

File(s) associated to this reference | ||||||||||||||

| ||||||||||||||

All documents in ORBi^{lu} are protected by a user license.