… modules. For example, we prove in Proposition 2.1 that a right R-module M is simple-direct-projective …
In Proposition 2.3, M is simple-direct-projective module if and only if whenever {X 1 …

… A right R-module M is called simple-direct-projective if, whenever, A and B are submodules
… of simple-direct-injective and simple-direct-projective modules has been carried out, and …

… modules have been studied like semi-projective modules and simple direct projective modules
… Motivated by these generalizations and work done in [13] on pure direct injective modules…

… In this paper, we characterize simple-direct-injective and simple-direct-projective modules
… iff every right module with zero Jacobson radical is simple-direct-projective. We prove that …

… simple-direct-projective modules are simple-directinjective if and only if simple-direct-injective
modules are simple-direct-projective … and some classes of modules that are simple-direct-…

… simple-direct-injective modules and simple-direct-projective modules over a formal matrix
… a \(K\)-module to be, respectively, simple-direct-injective or simple-direct-projective. We also …

… which are a generalization of injective modules unifies C2 and C3-modules. In the present
paper, we introduce the notion of the semisimple-direct-injective module which gives a unified …

… only if every 2-generated right R-module is a simple-direct-projective module if and only if
every direct sum of two simple-direct-projective modules is a simple-direct-projective module. …

… we obtain several equivalent conditions for modules to being simple-direct-injective and give
some properties of this type of modules. Among others, we prove that a module M is simple-…

… Let A be a ring (with a unit) and M be an A-module; we say also A , M is a module. We
are concerned about the ring of a module, since it is an essential fact in what follows. …