Regular completion of modules
Matematičeskie zametki, Tome 19 (1976) no. 6, pp. 843-851.

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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.
@article{MZM_1976_19_6_a2,
     author = {V. K. Zakharov},
     title = {Regular completion of modules},
     journal = {Matemati\v{c}eskie zametki},
     pages = {843--851},
     publisher = {mathdoc},
     volume = {19},
     number = {6},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_6_a2/}
}
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V. K. Zakharov. Regular completion of modules. Matematičeskie zametki, Tome 19 (1976) no. 6, pp. 843-851. http://geodesic.mathdoc.fr/item/MZM_1976_19_6_a2/