Prescribed behavior of central simple algebras after scalar extension
U Rehmann, SV Tikhonov, VI Yanchevskiĭ - Journal of Algebra, 2012 - Elsevier
U Rehmann, SV Tikhonov, VI Yanchevskiĭ
Journal of Algebra, 2012•Elsevier1. 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 [Formula: see text] and [Formula: see text], i= 1,…,
n. 2. Let A be a central simple algebra over a field K with an involution τ 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⊗ KE is cyclic and has an involution of the second kind extending τ.
(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 [Formula: see text] and [Formula: see text], i= 1,…,
n. 2. Let A be a central simple algebra over a field K with an involution τ 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⊗ KE is cyclic and has an involution of the second kind extending τ.
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 [Formula: see text] and [Formula: see text] , i=1,…,n. 2. Let A be a central simple algebra over a field K with an involution τ 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⊗KE is cyclic and has an involution of the second kind extending τ.
Elsevier
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