[en] Let K be a quadratic number field and let \alpha \in K*. We present an explicit finite procedure to compute at once all Kummer degrees [K(\zeta_m,\sqrt[n]{\alpha}):K(\zeta_m)] for n,m \geq 1 with n|m, where \zeta_m denotes a primitive m-th root of unity. We can also replace \alpha by any finitely generated subgroup of K*.
Disciplines :
Mathematics
Author, co-author :
Hörmann, Fritz; University of Freiburg > Mathematics
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 :
Explicit Kummer theory for quadratic fields
Publication date :
2021
Journal title :
JP Journal of Algebra, Number Theory and Applications
