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

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.

6 pages

References in corpus (1)

• Non-noetherian groups and primitivity of their group algebras

Cited by in corpus (1)

• Property $P_{naive}$ for acylindrically hyperbolic groups