  A partition of the set of unary pp formulas into four regions is presented,
which has a bearing on various structural properties of modules. The machinery
developed allows for applications to IF, weakly coherent, nonsingular, and
reduced rings, as well as domains, specifically Ore domains. One of the four
types of formula are called high. These are used to define Ulm submodules and
Ulm length of modules over any associative ring. It is shown that pure
injective modules have Ulm length at most 1. As a consequence, pure injective
modules over RD domains (in particular, pure injective modules over the first
Weyl algebra over a field of characteristic 0) are shown to decompose into a
largest injective and a reduced submodule. This study serves as preparation for
forthcoming work with A. Martsinkovsky on injective torsion.
