Normality is polynomial-closed
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).