# Does every strongly $\pi$-regular ring have artinian prime factors?

A ring $R$ is called strongly $\pi$-regular if for every element $r \in R$ there exists an element $x \in R$ such that $r^{n+1}x = r^n$ for some positive integer $n$. Meanwhile, a ring $R$ is said to have artinian prime factors if $R/P$ is artinian for every prime ideal $P$ of $R$. It is known that every ring with artinian prime factors is strongly $\pi$-regular. Does every strongly $\pi$-regular ring have artinian prime factors?

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