AI 中文总结
该研究证明了无混合恒等性且含非阿贝尔自由子群的可数群的群环为本原环，提出的动力学准则可复现已有结果并适用于类汤普森群等新群类。
AI 中文摘要
我们证明：每个无混合恒等性（MIF）且包含非阿贝尔自由子群的可数群G，对任意域K，其群环KG都是本原的。我们还给出一个纯动力学准则，该准则可推出此结果，且能复现若干现有本原性相关结果（包括涉及双曲 acylindrical 群的结果）。此外，该准则还适用于大量新例子，如类汤普森群、双曲群的可换子群、部分Kac-Moody群等。
英文摘要
We show that every countable group $G$ that is mixed-identity-free (MIF) and contains a non-abelian free subgroup has the following property: the group ring $KG$ is primitive for any field $K$. We also present a purely dynamical criterion that implies this result. Our criterion recovers several of the existing results on primitivity, including those involving acylindrically hyperbolic groups. Furthermore, our criterion also applies (positively) to a plethora of new examples, such as Thompson-like groups, commensurator groups of hyperbolic groups, some Kac-Moody groups, and many more.
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