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Transactions of the American Mathematical Society

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

 

 

Trace functions in the ring of fractions of polycyclic group rings


Author: A. I. Lichtman
Journal: Trans. Amer. Math. Soc. 330 (1992), 769-781
MSC: Primary 16S34; Secondary 20C07
DOI: https://doi.org/10.1090/S0002-9947-1992-1040264-7
MathSciNet review: 1040264
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Abstract: Let $ KG$ be the group ring of a polycyclic-by-finite group $ G$ over a field $ K$ of characteristic zero, $ R$ be the Goldie ring of fractions of $ KG$, $ S$ be an arbitrary subring of $ {R_{n \times n}}$. We prove that the intersection of the commutator subring $ [S,S]$ with the center $ Z(S)$ is nilpotent. This implies the existence of a nontrivial trace function in $ {R_{n \times n}}$.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1040264-7
Article copyright: © Copyright 1992 American Mathematical Society