Ertaş, Nil OrhanAcar, Ummahan2022-08-052022-08-0520210976-5905https://hdl.handle.net/20.500.12885/2016For two modules M and N, P-M(N) stands for the largest submodule of N relative to which M is projective. For any module M, P-M(N) defines a left exact preradical. It is given some properties of P-M(N). We express P-M(N) as a trace submodule. In this paper, we study rings with no quasi-projective modules other than semisimples and projectives, that is, rings whose quasi-projectives are either projective or semisimple (namely QPS-ring). Semi-Artinian rings and rings with no right p-middle class are characterized by using this functor: a ring R right semi-Artinian if and only if for any right R -module M, P-M(M) <=(e) M.eninfo:eu-repo/semantics/closedAccessProjective modulep-poor moduleProjectivity domainSemi-Artininan ringArticle10.26713/cma.v12i2.1490122295302N/A