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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The zero divisor problem for a class of torsion-free groups


Author: A. I. Lichtman
Journal: Proc. Amer. Math. Soc. 82 (1981), 188-190
MSC: Primary 16A27
MathSciNet review: 609648
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Abstract: Let $ G$ be a group, $ N$ be a central torsion-free subgroup of $ G$ and let $ R$ be an arbitrary field. Then $ R(G)$ contains no nilpotent elements provided that $ R(G/N)$ contains no nilpotent elements.

When $ G$ is torsion-free the conditions of the theorem imply that $ RG$ is a domain; this generalizes Passman's theorem in [1].


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DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0609648-0
Keywords: Groups, group rings
Article copyright: © Copyright 1981 American Mathematical Society