Definition 15.47.1. Let $R$ be a Noetherian ring. Let $X = \mathop{\mathrm{Spec}}(R)$.

We say $R$ is

*J-0*if $\text{Reg}(X)$ contains a nonempty open.We say $R$ is

*J-1*if $\text{Reg}(X)$ is open.We say $R$ is

*J-2*if any finite type $R$-algebra is J-1.

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