Definition:Jacobson Ring

Definition
Let $\left({R, +, \circ}\right)$ be a commutative ring with unity.

Then $\left({R, +, \circ}\right)$ is a Jacobson ring iff:
 * every prime ideal of $\left({R, +, \circ}\right)$ is an intersection of maximal ideals.

Also known as
It is also known as a Hilbert ring, for David Hilbert.

The term was coined by Wolfgang Krull in honour of Jacobson's work on the Jacobson radical.