Definition: Prime ideals are intersections of maximal ideals. Also known as: Hilbert rings

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- passes to finitely generated algebras over the ring
- passes to polynomial rings

- passes to subrings (Counterexample: $R_{ 69 }$ is a subring of $R_{ 2 }$)

Rings

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- = has the property
- = does not have the property
- = information not in database