Jacobson is polynomial-closed

From Commalg

This article gives the statement, and possibly proof, of a commutative unital ring property satisfying a commutative unital ring metaproperty
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Statement

Verbal statement

The polynomial ring over a Jacobson ring is again a Jacobson ring.

Proof

Let be a Jacobson ring. In other words, every prime ideal of is expressible as an intersection of maximal ideals.