Central zero divisors in group algebras
HTML articles powered by AMS MathViewer
- by Martha K. Smith
- Proc. Amer. Math. Soc. 91 (1984), 529-531
- DOI: https://doi.org/10.1090/S0002-9939-1984-0746082-X
- PDF | Request permission
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
- K. R. Goodearl, Localized group rings, the invariant basis property and Euler characteristics, Proc. Amer. Math. Soc. 91 (1984), no. 4, 523–528. MR 746081, DOI 10.1090/S0002-9939-1984-0746081-8
- Donald S. Passman, The algebraic structure of group rings, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1977. MR 0470211
Bibliographic Information
- © Copyright 1984 American Mathematical Society
- 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