On M-injective and M-projective Modules

Abstract

In this study, the concept of m-projective modules is introduced. A right R-module M is said to be m-projective if Ext(M,N)=0 for any m-injective right R-module N. We prove that every right R-module has a special m-projective precover and m-injective preenvelope. We characterize C-rings, SF-rings and max-hereditary rings using m-projective and m-injective modules.