Alagoz, YusufBenli, SinemBuyukasik, Engin2024-12-242024-12-2420210010-26281213-7243https://doi.org/10.14712/1213-7243.2021.036https://hdl.handle.net/20.500.12604/7351A right R-module M is called R-projective provided that it is projective relative to the right R-module R-R. This paper deals with the rings whose all nonsingular right modules are R-projective. For a right nonsingular ring R, we prove that R-R is of finite Goldie rank and all nonsingular right R-modules are R-projective if and only if R is right finitely Sigma-CS and fiat right R-modules are R-projective. Then, R-projectivity of the class of nonsingular injective right modules is also considered. Over right nonsingular rings of finite right Goldie rank, it is shown that R-projectivity of nonsingular injective right modules is equivalent to R-projectivity of the injective hull E(R-R). In this case, the injective hull E(R-R) has the decomposition E(R-R) = U-R circle plus V-R, where U is projective and Hom(V, R/I) = 0 for each right ideal I of R. Finally, we focus on the right orthogonal class N-perpendicular to of the class IV of nonsingular right modules.eninfo:eu-repo/semantics/openAccessnonsingular moduleR-projective moduleflat moduleperfect ringArticle624393407N/AWOS:000818514600001Q42-s2.0-8512503746810.14712/1213-7243.2021.036