On Maximal Relatively Divisible Submodules

In recent work Goebel and Goldsmith investigated the spectrum of maximal pure subgroups of certain Abelian groups. Here the situation relating to maximal pure submodules of a torsion-free module over an integral domain R is investigated. Connections to the level of coherency are established along with a detailed investigation of the situation where all maximal pure submodules are isomorphic to a product of copies of the ring R.