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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 is a semisimple artinian ring if and only if is SIP and every right -module has a SIP-cover. We also prove that is a semiregular ring and if only if every finitely generated projective module is a SIP-CS module which is also a module.