Ulf Rehmann, Sergey V. Tikhonov, and Vyacheslav I. Yanchevskii: Prescribed behavior of central simple algebras after scalar extension

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 A1,...,An be central simple disjoint algebras over a field F. Let also li | exp( Ai ), mi | ind( Ai ), li | mi, and, for each i=1,...,n, let li and mi have the same sets of prime divisors. Then there exists a field extension E/F such that exp(AiE) = li and ind(AiE) = mi, 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 AE 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

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