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Zero divisors and idempotents in group rings

Published online by Cambridge University Press:  24 October 2008

P. A. Linnell
P. A. Linnell
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge
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1. Introduction. Let kG denote the group algebra of a group G over a field k. In this paper we are first concerned with the zero divisor conjecture: that if G is torsion free, then kG is a domain. Recently, K. A. Brown made a remarkable breakthrough when he settled the conjecture for char k = 0 and G abelian by finite (2). In a beautiful paper written shortly afterwards, D. Farkas and R. Snider extended this result to give an affirmative answer to the conjecture for char k = 0 and G polycyclic by finite. Their methods, however, were less successful when k had prime characteristic. We use the techniques of (4) and (7) to prove the following:

Theorem A. If G is a torsion free abelian by locally finite by supersoluble group and k is any field, then kG is a domain.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 81 , Issue 3 , May 1977 , pp. 365 - 368
Copyright
Copyright © Cambridge Philosophical Society 1977

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References

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