Definition:Jacobson Ring

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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.

Also see