  In this paper, we investigate some properties of SIP, SSP and CS-Rickart
modules. We give equivalent conditions for SIP and SSP modules; establish
connections between the class of semisimple artinian rings and the class of SIP
rings. It shows that $R$ is a semisimple artinian ring if and only if $R_R$ is
SIP and every right $R$-module has a SIP-cover. We also prove that $R$ is a
semiregular ring and $J(R) = Z(R_R)$ if only if every finitely generated
projective module is a SIP-CS module which is also a $C2$ module.
