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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The Brauer group is torsion


Author: David J. Saltman
Journal: Proc. Amer. Math. Soc. 81 (1981), 385-387
MSC: Primary 16A16; Secondary 13A20
DOI: https://doi.org/10.1090/S0002-9939-1981-0597646-5
MathSciNet review: 597646
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Abstract: We present a new proof that if $ A$ is an Azumaya algebra over a commutative ring $ R$ of rank $ {n^2}$, then $ {A^n} = A{ \otimes _R} \cdots { \otimes _R}A$ is a split Azumaya algebra $ {\text{En}}{{\text{d}}_R}(P)$. We provide a description of $ P$, including that it is a direct summand of $ {A^n}$.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0597646-5
Keywords: Azumaya algebra, Brauer group
Article copyright: © Copyright 1981 American Mathematical Society

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