Article (Scientific journals)
The degree of Kummer extensions of number fields
Perucca, Antonella; Sgobba, Pietro; Tronto, Sebastiano
2021In International Journal of Number Theory
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Keywords :
number field; Kummer theory; degree; Kummer extension
Abstract :
[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.
Disciplines :
Mathematics
Author, co-author :
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
External co-authors :
yes
Language :
English
Title :
The degree of Kummer extensions of number fields
Publication date :
2021
Journal title :
International Journal of Number Theory
ISSN :
1793-0421
Publisher :
World Scientific Publishing Co., Singapore
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBilu :
since 11 February 2020

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