Modules close to SSP- and SIP-modules

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.