In commutative algebra, a J-0 ring is a ring R {\displaystyle R} such that the set of regular points, that is, points p {\displaystyle p} of the spectrum at which the localization R p {\displaystyle R_{p}} is a regular local ring, contains a non-empty open subset, a J-1 ring is a ring such that the set of regular points is an open subset, and a J-2 ring is a ring such that any finitely generated algebra over the ring is a J-1 ring. Wikipedia