Catenary ring

This article defines a property of commutative rings

Definition

A commutative unital ring is said to be catenary if it satisfies the following condition:

If $P<P_1<P_2<Q$ is a strictly ascending chain of prime ideals, and $P^{\prime }$ is a prime ideal between $P$ and $Q$, then there is either a prime ideal between $P$ and $P^{\prime }$ or a prime ideal between $P^{\prime }$ and $Q$.

Relation with other properties

Stronger properties

• Affine ring