Polynomial-closed property

This is a category of properties for the following kind of objects: [[Category:Polynomial-closed properties of commutative rings]]s. In other words, this category lists [[Category:Polynomial-closed properties of commutative rings metaproperty|Category:Polynomial-closed properties of commutative rings metaproperties]]
All articles in subcategories of this category are also directly included in this category
View a complete list of metaproperty categories

Definition

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 $R[x]$.