Coherence classes of ideals of normal lattices with applications to C(X)

Given a topological space X, Jenkins and McKnight have shown how ideals of the ring C(X) are partitioned into equivalence classes — called coherence classes — defined by declaring ideals to be equivalent if their pure parts are identical. In this paper we consider a similar partitioning of the lattice of ideals of a normal bounded distributive lattice. We then apply results obtained herein to augment some of those of Jenkins and McKnight. In particular, for Tychonoff spaces, new results include the following:

1. all members of any coherence class have the same annihilator
2. every ideal is alone in its coherence class if and only if the space is a P-space.