Catenary ring

This article defines a property of commutative rings

Definition

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

If $P<P_{1}<P_{2}<Q$ is a strictly ascending chain of prime ideals, and $P'$ is a prime ideal between $P$ and $Q$, then there is either a prime ideal between $P$ and $P'$ or a prime ideal between $P'$ and $Q$.

Relation with other properties

Stronger properties

• Affine ring