Alagoz, YusufBenli-Goral, SinemBuyukasik, Engin2024-12-242024-12-2420230219-49881793-6829https://doi.org/10.1142/S0219498823501384https://hdl.handle.net/20.500.12604/7226For a right module M, we prove that M is simple-injective if and only if M is min-N-injective for every cyclic right module N. The rings whose simple-injective right modules are injective are exactly the right Artinian rings. A right Noetherian ring is right Artinian if and only if every cyclic simple-injective right module is injective. The ring is QF if and only if simple-injective right modules are projective. For a commutative Noetherian ring R, we prove that every finitely generated simple-injective R-module is projective if and only if R = A x B, where A is QF and B is hereditary. An abelian group is simple-injective if and only if its torsion part is injective. We show that the notions of simple-injective, strongly simple-injective, soc-injective and strongly soc-injective coincide over the ring of integers.eninfo:eu-repo/semantics/closedAccess(Min) injective modulessimple-injective modulesArtinian ringsArticle226Q3WOS:000849402000003Q22-s2.0-8512901200410.1142/S0219498823501384