Abstract
A right R-module M is called simple-direct-injective if, whenever, A and B are simple submodules of M with A≅B, and B⊆
⊕
M, then A⊆
⊕
M. Dually, M is called simple-direct-projective if, whenever, A and B are submodules of M with M∕A≅B⊆
⊕
M and B simple, then A⊆
⊕
M. In this paper, we continue our investigation of these classes of modules strengthening many of the established results on the subject. For example, we show that a ring R is uniserial (artinian serial) with J
2
(R) = 0 iff every simple-direct-projective right R-module is an SSP-module (SIP-module) iff every simple-direct-injective right R-module is an SIP-module (SSP-module).