# Normality is polynomial-closed

From Commalg

This article gives the statement, and possibly proof, of a commutative unital ring property (i.e., normal ring) satisfying a commutative unital ring metaproperty (i.e., polynomial-closed property of commutative unital rings)

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This article gives the statement, and possibly proof, of a integral domain property (i.e., normal domain) satisfying a integral domain metaproperty (i.e., polynomial-closed property of integral domains)

View all integral domain metaproperty satisfactions | View all integral domain metaproperty dissatisfactions |Get help on looking up metaproperty (dis)satisfactions for integral domain properties

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## Statement

### For commutative unital rings

The polynomial ring over a normal ring is also a normal ring.

### For integral domains

The polynomial ring over a normal domain is also a normal domain.

## Facts used

## Proof

The proof follows directly from fact (1).