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

DOI:
https://doi.org/10.1090/S0002-9947-1987-0869417-3

MathSciNet review:
869417

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Abstract | References | Similar Articles | Additional Information

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 of a residually torsion free nilpotent group . It is shown that its subfield , generated by the group ring , does not depend on the order of for many kinds of orders and the study of can be reduced in some sense to the case when is nilpotent.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1987-0869417-3

Keywords:
Group rings,
skew fields,
free products,
ordered groups,
residually nilpotent groups

Article copyright:
© Copyright 1987
American Mathematical Society