Semisimple-direct-injective modules

The notion of simple-direct-injective modules which are a generalization injective unifies $C2$ and $C3$-modules. In the present paper, we introduce semisimple-direct-injective module gives unified viewpoint $C2$, $C3$, SSP properties modules. It is proved that ring $R$ Artinian serial with Jacobson radical square zero if only every right $R$-module has and, for any family simple $R$-modules $\{S_i\}_{\mathcal{I}}$, $\oplus_{\mathcal{I}}S_i$ injective. We also show Noetherian V-ring envelope cover.