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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Zero divisors in tensor products of division algebras


Author: Lawence J. Risman
Journal: Proc. Amer. Math. Soc. 51 (1975), 35-36
MSC: Primary 12A80; Secondary 16A40
MathSciNet review: 0374101
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Abstract: Theorem. If a tensor product of a division algebra $ D$ with a quaternion algebra $ Q$ is not a division algebra, then either $ D$ and $ Q$ possess a common quadratic subfield or $ D$ contains a splitting field of $ Q$ not quadratic over the base field.

The above theorem generalizes a recently published result of Albert's.

Theorem. If the tensor product of two division algebras over a local or a global field $ K$ is not a division algebra, then they contain a common extension field of $ K$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0374101-6
PII: S 0002-9939(1975)0374101-6
Article copyright: © Copyright 1975 American Mathematical Society