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Splitting of Algebras by Function Fields of One Variable

Published online by Cambridge University Press:  22 January 2016

Peter Roquette
Peter Roquette*
Affiliation:
Tübingen University, Germany
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Let K be a field and (K) the Brauer group of K. It consists of the similarity classes of finite central simple algebras over K. For any field extension F/K there is a natural mapping (K) → (F) which is obtained by assigning to each central simple algebra A/K the tensor product which is a central simple algebra over F. The kernel of this map is the relative Brauer group (F/K), consisting of those A ∈(K) which are split by F.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 2 , July 1966 , pp. 625 - 642
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

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