Pure submodules of finite direct sums of co-purely indecomposable modules

A torsion-free module M of finite rank over a discrete valuation ring R with prime p is co-purely indecomposable if M is indecomposable and rank M = 1 + dim(R/pR) (M/pM). Co-purely indecomposable modules are duals of pure finite rank submodules of the p-adic completion of R. Pure submodules of epi-decomposable modules (finite direct sums of co-purely indecomposable moduks) are characterized. Included are various examples and properties of these modules.