Refail AlizadeSultan Eylem Toksoy2025-10-06202402194988, 179368290219-49881793-682910.1142/S0219498824500105https://www.scopus.com/inward/record.uri?eid=2-s2.0-85140872509&doi=10.1142%2FS0219498824500105&partnerID=40&md5=4a4fcd6e7dc43042db051d405384db25https://gcris.yasar.edu.tr/handle/123456789/8354In 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 Rmodule 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. © 2023 Elsevier B.V. All rights reserved.English(pure-)direct-projective Modules, (pure-)projective Modules, Von Neumann Regular RingsArticle