 

Karim Johannes Becher and
Fatma Kader Bingol
A bound on the index of exponent4 algebras in terms of the uinvariant
view
print


Published: 
December 7, 2023. 
Keywords: 
Brauer group, cyclic algebra, symbol length, index, exponent, uinvariant. 
Subject [2020]: 
12E15, 16K20, 16K50. 


Abstract
For a prime number p, an integer e > 1 and a field F containing a primitive
p^{e}th root of unity, the index of central simple Falgebras of exponent
p^{e} is bounded in terms of the psymbol length of F. For a nonreal field
F of characteristic different from 2, the index of central simple algebras of exponent
4 is bounded in terms of the uinvariant of F. Finally, a new construction for nonreal
fields of uinvariant 6 is presented.


Acknowledgements
We thank the referee for their comments.
This work was supported by the Fonds Wetenschappelijk OnderzoekVlaanderen
(FWO) in the FWO Odysseus Programme (project G0E6114N 'Explicit Methods in
Quadratic Form Theory'), the Fondazione Cariverona in the programme Ricerca Scientifica di Eccellenza 2018 (project 'Reducing complexity in algebra, logic, combinatorics  REDCOM'), and by the FWOTournesol programme (project VS05018N).


Author information
Karim Johannes Becher
University of Antwerp
Department of Mathematics
Middelheimlaan 1, 2020 Antwerpen, Belgium
KarimJohannes.Becher@uantwerpen.be
Fatma Kader Bingol
University of Antwerp
Department of Mathematics
Middelheimlaan 1, 2020 Antwerpen, Belgium
FatmaKader.Bingol@uantwerpen.be

