# Definition:Jacobson Ring

(Redirected from Definition:Hilbert Ring)

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## Definition

Let $\struct {R, +, \circ}$ be a commutative ring with unity.

Then $\struct {R, +, \circ}$ is a **Jacobson ring** if and only if:

- every prime ideal of $\struct {R, +, \circ}$ is an intersection of maximal ideals.

## Also known as

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

## Also see

## Source of Name

This entry was named for Nathan Jacobson.

## Historical Note

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