Prescribed behavior of central simple algebras after scalar extension

Rehmann U, Tikhonov SV, Yanchevskii VI (2012)
Journal of Algebra 351(1): 279-293.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Rehmann, UlfUniBi; Tikhonov, Sergey V.; Yanchevskii, Vyacheslav I.
Abstract / Bemerkung
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.
Stichworte
Brauer groups; Splitting theory; Central simple algebras
Erscheinungsjahr
2012
Zeitschriftentitel
Journal of Algebra
Band
351
Ausgabe
1
Seite(n)
279-293
ISSN
0021-8693
Page URI
https://pub.uni-bielefeld.de/record/2474350

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Rehmann U, Tikhonov SV, Yanchevskii VI. Prescribed behavior of central simple algebras after scalar extension. Journal of Algebra. 2012;351(1):279-293.
Rehmann, U., Tikhonov, S. V., & Yanchevskii, V. I. (2012). Prescribed behavior of central simple algebras after scalar extension. Journal of Algebra, 351(1), 279-293. doi:10.1016/j.jalgebra.2011.11.027
Rehmann, U., Tikhonov, S. V., and Yanchevskii, V. I. (2012). Prescribed behavior of central simple algebras after scalar extension. Journal of Algebra 351, 279-293.
Rehmann, U., Tikhonov, S.V., & Yanchevskii, V.I., 2012. Prescribed behavior of central simple algebras after scalar extension. Journal of Algebra, 351(1), p 279-293.
U. Rehmann, S.V. Tikhonov, and V.I. Yanchevskii, “Prescribed behavior of central simple algebras after scalar extension”, Journal of Algebra, vol. 351, 2012, pp. 279-293.
Rehmann, U., Tikhonov, S.V., Yanchevskii, V.I.: Prescribed behavior of central simple algebras after scalar extension. Journal of Algebra. 351, 279-293 (2012).
Rehmann, Ulf, Tikhonov, Sergey V., and Yanchevskii, Vyacheslav I. “Prescribed behavior of central simple algebras after scalar extension”. Journal of Algebra 351.1 (2012): 279-293.

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