Trace functions in the ring of fractions of polycyclic group rings

Lichtman, A. I.

doi:10.1090/S0002-9947-1992-1040264-7

Trace functions in the ring of fractions of polycyclic group rings
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by A. I. Lichtman

Trans. Amer. Math. Soc. 330 (1992), 769-781

DOI: https://doi.org/10.1090/S0002-9947-1992-1040264-7

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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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