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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On embedding of group rings of residually torsion free nilpotent groups into skew fields


Authors: A. Eizenbud and A. I. Lichtman
Journal: Trans. Amer. Math. Soc. 299 (1987), 373-386
MSC: Primary 16A27; Secondary 16A08, 16A39, 20C07
MathSciNet review: 869417
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Abstract: It is proven that the group ring of an amalgamated free product of residually torsion free nilpotent groups is a domain and can be embedded in a skew field. This is a generalization of J. Lewin's theorem, proven for the case of free groups. Our proof is based on the study of the Malcev-Neumann power series ring $ K\left\langle G \right\rangle $ of a residually torsion free nilpotent group $ G$. It is shown that its subfield $ D$, generated by the group ring $ KG$, does not depend on the order of $ G$ for many kinds of orders and the study of $ D$ can be reduced in some sense to the case when $ G$ is nilpotent.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0869417-3
PII: S 0002-9947(1987)0869417-3
Keywords: Group rings, skew fields, free products, ordered groups, residually nilpotent groups
Article copyright: © Copyright 1987 American Mathematical Society