Reference : Explicit Kummer theory for quadratic fields
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/42266
Explicit Kummer theory for quadratic fields
English
Hörmann, Fritz mailto [University of Freiburg > Mathematics]
Perucca, Antonella mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Sgobba, Pietro mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Tronto, Sebastiano mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2021
JP Journal of Algebra, Number Theory and Applications
Pushpa Publishing House
Yes
International
0972-5555
India
[en] Kummer theory ; Kummer extension ; number field ; cyclotomic field ; quadratic field ; degree
[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*.
Researchers
http://hdl.handle.net/10993/42266

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