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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 a theorem of Flanders

Author: Robert E. Hartwig
Journal: Proc. Amer. Math. Soc. 85 (1982), 310-312
MSC: Primary 15A21; Secondary 15A09
MathSciNet review: 656090
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Abstract: It is shown that if $ R$ is a regular strongly-pi-regular ring, then $ R$ is unit-regular precisely when $ {(ab)^d} \approx {(ba)^d}$ for all $ a, b \in R$. This generalizes a result by Flanders, which states that the matrices $ AB$ and $ BA$ over a field $ {\mathbf{F}}$ have the same elementary divisors except possibly those divisible by $ \lambda $.

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PII: S 0002-9939(1982)0656090-3
Article copyright: © Copyright 1982 American Mathematical Society