In this paper we introduce the concept of a module regular in the sense of von Neumann. We construct a regular completion of a module X torsion-free relative to a filter\(\mathfrak{F}_R \) of dense modules over a commutative semiprimary ring R. The paper's main result is a theorem that module X is divisible (is injective relative to filter\(\mathfrak{F}_R \)) if and only if it is von Neumann-regular and orthocomplete. We prove that a divisible hull of module X relative to\(\mathfrak{F}_R \) is a composition of two simpler completions: a regular one and an orthocompletion.