Çelik, CesimÖzen, TahireAgayev, Nazım2021-06-232021-06-2320180253-41420973-7685https://doi.org/10.1007/s12044-018-0403-6https://hdl.handle.net/20.500.12491/9627Let R be a ring with identity. A module M-R is called an r-semisimple module if for any right ideal I of R, MI is a direct summand of M-R which is a generalization of semisimple and second modules. We investigate when an r-semisimple ring is semisimple and prove that a ring R with the number of nonzero proper ideals <= 4 and J (R) = 0 is r-semisimple. Moreover, we prove that R is an r-semisimple ring if and only if it is a direct sum of simple rings and we investigate the structure of module whenever R is an r-semisimple ring.eninfo:eu-repo/semantics/closedAccessSemisimple ModulesSecond ModulesInjective ModulesArticle10.1007/s12044-018-0403-612822-s2.0-85046436967Q3WOS:000431455500001Q4