Universally catenary ring

This article defines a property of commutative unital rings; a property that can be evaluated for a commutative unital ring
View all properties of commutative unital rings
VIEW RELATED: Commutative unital ring property implications | Commutative unital ring property non-implications |Commutative unital ring metaproperty satisfactions | Commutative unital ring metaproperty dissatisfactions | Commutative unital ring property satisfactions | Commutative unital ring property dissatisfactions

Definition

A commutative unital ring is termed universally catenary if it satisfies the following equivalent conditions:

• Every finitely generated algebra over it is a catenary ring
• Every polynomial ring in finitely many variables, over it, is a catenary ring

Relation with other properties

Stronger properties

• Cohen-Macaulay ring

Weaker properties

• Catenary ring
• Noetherian ring

Metaproperties

Closure under taking quotient rings

This property of commutative unital rings is quotient-closed: the quotient ring of any ring with this property, by any ideal in it, also has this property

View other quotient-closed properties of commutative unital rings