rehmann@math.uni-bielefeld.de, tsv@im.bas-net.by, yanch@imbas-net.by

Submission: 2010, Dec 7, revised 2011, Oct 9, to appear in J. Alg.

1. Let A_{1},...,A_{n} be central simple disjoint algebras over
a field F. Let also l_{i} | exp( A_{i} ), m_{i} | ind( A_{i} ), l_{i} |
m_{i}, and, for each i=1,...,n, let l_{i} and m_{i} have the same
sets of prime divisors.
Then there exists a field extension E/F such
that exp(A_{i}_{E}) = l_{i} and ind(A_{i}_{E}) = m_{i}, i=1,...,n.

2. Let A be a central simple algebra over a field K
with an involution \tau of the second kind. We prove
that there exists a regular field
extension E/K preserving indices of central simple K-algebras such that A_{E} is cyclic and has an involution of the second kind extending \tau.

2000 Mathematics Subject Classification: 16Kxx, 12E15

Keywords and Phrases: Central simple agebras, Brauer groups, splitting theory

Full text: dvi.gz 32 k, dvi 76 k, ps.gz 1013 k, pdf.gz 170 k, pdf 196 k.

Server Home Page