Rafail AlizadeSultan Eylem ToksoyAlizade, RafailToksoy, Sultan Eylem2025-10-0620240219-49881793-682910.1142/S02194988245001052-s2.0-85140872509http://dx.doi.org/10.1142/S0219498824500105https://gcris.yasar.edu.tr/handle/123456789/7095https://doi.org/10.1142/S0219498824500105In this paper we introduce and study the pure-direct-projective modules that is the modules M every pure submodule A of which with M/A isomorphic to a direct summand of M is a direct summand of M. We characterize rings over which every right R-module is pure-direct-projective. We examine for which rings or under what conditions pure-direct-projective right R-modules are direct-projective projective quasi-projective pure-projective flat or injective. We prove that over a Noetherian ring every injective module is pure-direct-projective and a right hereditary ring R is right Noetherian if and only if every injective right R-module is pure-direct-projective. We obtain some properties of pure-direct-projective right R-modules which have DPSP and DPIP.Englishinfo:eu-repo/semantics/closedAccess(Pure-)direct-projective modules, (pure-)projective modules, von Neumann regular ringsRINGSVon Neumann Regular Rings(Pure-)Projective Modules(Pure-)Direct-Projective ModulesArticle