Modules close to SSP- and SIP-modules

摘要

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