PUB - Publikationen an der Universität Bielefeld

1. Let A(1), ..., A(n) be central simple disjoint algebras over a field F. Let also |(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(Ai(E)) = l(i) and ind(A(iE)) = 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 circle times(K) E is cyclic and has an involution of the second kind extending tau. (C) 2011 Elsevier Inc. All rights reserved.