Definition:Jacobson 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.
Sources
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