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

Central zero divisors in group algebras


Author: Martha K. Smith
Journal: Proc. Amer. Math. Soc. 91 (1984), 529-531
MSC: Primary 16A27; Secondary 16A08, 22D25, 43A10, 46L99
MathSciNet review: 746082
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Abstract: A central element of the complex group algebra $ {\mathbf{C}}G$ which is a zero divisor in the $ {W^ * }$ group algebra $ W(G)$ is also a zero divisor in $ {\mathbf{C}}G$. As a corollary, if $ K$ is a field of characteristic zero, $ G$ is a group, $ A$ is an abelian normal subgroup of $ G$, and $ R$ is the Ore localization of $ KG$ obtained by inverting all nonzero elements of $ KA$, then all matrix rings over $ R$ are directly finite and $ R$ has the invariant basis property.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0746082-X
PII: S 0002-9939(1984)0746082-X
Article copyright: © Copyright 1984 American Mathematical Society