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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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On embedding of group rings of residually torsion free nilpotent groups into skew fields
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by A. Eizenbud and A. I. Lichtman PDF
Trans. Amer. Math. Soc. 299 (1987), 373-386 Request permission

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
  • © Copyright 1987 American Mathematical Society
  • 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