In algebra, a Hilbert ring or a Jacobson ring is a ring such that every prime ideal is an intersection of primitive ideals. For commutative rings primitive ideals are the same as maximal ideals so in this case a Jacobson ring is one in which every prime ideal is an intersection of maximal ideals.
Jacobson rings were introduced independently by Wolfgang Krull (1951, 1952), who named them after Nathan Jacobson because of their relation to Jacobson radicals, and by Oscar Goldman (1951), who named them Hilbert rings after David Hilbert because of their relation to Hilbert's Nullstellensatz.