Abstract
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 RR 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 CSRickart module which is also a C2 module.
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