# Definition:Jacobson Ring

## Definition

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

Then $\left({R, +, \circ}\right)$ is a Jacobson ring if and only if:

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.

## Source of Name

This entry was named for Nathan Jacobson.

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