Necessary and sufficient conditions so that a commutative ring can be embedded into a strongly pi-regular ring

If R is commutative ring then R can be embedded into a strongly $\pi$-regular ring if and only if there exists a set of prime ideals Y = $\{$P$\sb\alpha\}\alpha\in\Lambda$ and for each P$\sb\alpha$, a P$\sb\alpha$-primary ideal Q$\sb\alpha$ such that: (I) Y is closed in the patch topology on Spec R.