Examples of noncatenary rings

Abstract

A technique is developed for constructing a new family of noetherian integral domains. To each domain, there naturally corresponds its poset (partially ordered set) of prime ideals. The resulting family of posets has the following property: every finite poset is isomorphic to a saturated subset of some poset in the family. In the process, it is determined when certain power series may be adjoined to noetherian rings without destroying the noetherian property.