Catenary ring

Summary

A catenary ring is a commutative ring in which, between any two nested prime ideals, all maximal chains of primes have the same finite length. In such a ring the distance between two primes is well defined. Most rings met in practice are catenary, such as finitely generated algebras over a field and Cohen–Macaulay rings. Nagata showed that some Noetherian local domains are not catenary.