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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Zero divisors in tensor products of division algebras
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by Lawence J. Risman PDF
Proc. Amer. Math. Soc. 51 (1975), 35-36 Request permission

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
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 51 (1975), 35-36
  • MSC: Primary 12A80; Secondary 16A40
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0374101-6
  • MathSciNet review: 0374101