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
Abstract: A central element of the complex group algebra which is a zero divisor in the group algebra is also a zero divisor in . As a corollary, if is a field of characteristic zero, is a group, is an abelian normal subgroup of , and is the Ore localization of obtained by inverting all nonzero elements of , then all matrix rings over are directly finite and has the invariant basis property.
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-  Donald S. Passman, The algebraic structure of group rings, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1977. MR 470211