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arXiv · 1706.03905

Primitivity of group rings of non-elementary torsion-free hyperbolic groups

Brent B. Solie
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Abstract

We use a recent result of Alexander and Nishinaka to show that if $G$ is a non-elementary torsion-free hyperbolic group and $R$ is a countable domain, then the group ring $RG$ is primitive. This implies that the group ring $KG$ of any non-elementary torsion-free hyperbolic group $G$ over a field $K$ is primitive.

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Brent B. Solie. 2017-06-13. Primitivity of group rings of non-elementary torsion-free hyperbolic groups. https://doi.org/10.1016/j.jalgebra.2017.09.034

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