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A Note on Group Rings of Certain Torsion-Free Groups

Published online by Cambridge University Press:  20 November 2018

R. G. Burns  and
V. W. D. Hale
R. G. Burns
Affiliation:
York University, Downsview, Ontario
V. W. D. Hale
Affiliation:
University of York, York, U.K.
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Abstract

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As a step towards characterizing ID-groups (i.e., groups G such that, for every ring R without zero-divisors, the group ring RG has no zero-divisors), Rudin and Schneider defined Ω-groups, a possibly wider class than that of right-orderable groups, and proved that if every non-trivial finitely generated subgroup of a group G has a non-trivial H-group as an epimorphic image, then G is an ID-group. We prove that such groups are even Ω-groups and obtain the analogous result for right-orderable groups.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 3 , September 1972 , pp. 441 - 445
Copyright
Copyright © Canadian Mathematical Society 1972

References

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