AI 中文总结
本文证明具有小泽性质PHP且含非阿贝尔自由子群的可数群的群环对任意域本原，并推论非平凡可数线性群若具有平凡可和根则也满足此性质，同时建立了PHP类的一些永久性质。
AI 中文摘要
我们证明，每个具有小泽性质$\ m PHP$且包含非阿贝尔自由子群的可数群$G$具有以下性质：对任意域$K$，群环$KG$是本原的。作为推论，我们得出所有具有平凡可和根的、非平凡的可数线性群都具有此性质。在此过程中，我们证明了具有$\ m PHP$的群类享有某些具有独立意义的永久性质。
英文摘要
We show that every countable group $G$ that has Ozawa's property $\rm PHP$ and contains a non-abelian free subgroup has the following property: the group ring $KG$ is primitive for any field $K$. As a consequence, we deduce that all non-trivial countable linear groups with trivial amenable radical have this property. Along the way, we prove that the class of groups with $\rm PHP$ enjoys some permanence properties that are of independent interest.
Comments9 pages. Comments welcome!
