Definition:Jacobson Ring

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

• Definition:Jacobson Radical

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.