Moradzadeh-Dehkordi, AliAlagoz, Yusuf2024-09-182024-09-1820240009-725X1973-4409https://doi.org/10.1007/s12215-024-01089-1https://hdl.handle.net/20.500.12483/11987Given modules M and A, M is said to be A-RD-subinjective if for every RD-extension B of A, every f is an element of Hom(A,M) extends to Hom(B,M). For a module M, the RD-subinjectivity domain of M is defined to be the collection of all modules A such that M is A-RD-subinjective. We investigate basic properties of RD-subinjectivity domains and provide characterizations for various types of rings and modules including p-injective modules, RD-coflat modules, von Neumann regular rings, RD-rings, Kothe rings, right Noetherian rings, and quasi-Frobenius rings in terms of RD-subinjectivity domains. Finally, we study the properties of RD-indigent modules and consider the structure of rings over which every (resp. simple) right module is RD-injective or RD-indigent.eninfo:eu-repo/semantics/closedAccessRD-injective moduleA-RD-subinjective moduleRD-subinjectivity domainRD-indigent moduleKothe ringArticle10.1007/s12215-024-01089-12-s2.0-85199293427Q1WOS:001275219700003N/A