Polynomial-closed property

Symbol-free definition
A property of commutative unital rings is termed polynomial-closed if whenever a commutative unital ring satisfies the property, so does the polynomial ring in one variable over that ring.

Definition with symbols
A property $$p$$ of commutative unital rings is termed polynomial-closed if whenever $$R$$ is a commutative unital ring satisfying $$p$$, so is $$R[x]$$.