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

 

On tensor products and extended centroids


Authors: W. K. Nicholson and J. F. Watters
Journal: Proc. Amer. Math. Soc. 88 (1983), 215-217
MSC: Primary 16A12; Secondary 16A20
MathSciNet review: 695244
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Abstract: For prime algebras $ R$ and $ S$ over a field $ F$ it is shown that each nonzero ideal of $ R \otimes S$ contains a nonzero element $ r \otimes s$, $ r \in R$, $ s \in S$, if and only if $ C(R) \otimes C(S)$ is a field, where $ C(R)$ (respectively $ C(S)$) is the extended centroid of $ R$ (respectively $ S$).


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0695244-8
PII: S 0002-9939(1983)0695244-8
Article copyright: © Copyright 1983 American Mathematical Society