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Proceedings of the American Mathematical Society

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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
DOI: https://doi.org/10.1090/S0002-9939-1984-0746082-X
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.


References [Enhancements On Off] (What's this?)

  • [1] K. R. Goodearl, Localized group rings, the invariant basis property and Euler characteristics, Proc. Amer. Math. Soc. 91 (1984), 523-528. MR 746081 (85e:16016)
  • [2] D. S. Passman, The algebraic structure of group rings, Wiley, New York, 1977. MR 470211 (81d:16001)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0746082-X
Article copyright: © Copyright 1984 American Mathematical Society

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