scholarly journals Orthogonal involutions on central simple algebras and function fields of Severi–Brauer varieties

2018 ◽  
Vol 336 ◽  
pp. 455-476
Author(s):  
Anne Quéguiner-Mathieu ◽  
Jean-Pierre Tignol
Keyword(s):  
Function Fields ◽  
Central Simple Algebras ◽  
Simple Algebras ◽  
Central Simple ◽  
And Function

scholarly journals Splitting of Algebras by Function Fields of One Variable

1966 ◽  
Vol 27 (2) ◽  
pp. 625-642 ◽  
Author(s):  
Peter Roquette
Keyword(s):  
Tensor Product ◽  
Function Fields ◽  
Central Simple Algebra ◽  
Simple Algebra ◽  
Field Extension ◽  
Brauer Group ◽  
Central Simple Algebras ◽  
Natural Mapping ◽  
Simple Algebras ◽  
Central Simple

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.

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