Modules close to SSP- and SIP-modules

Abyzov Adel; Tran Hoai Ngoc Nhan; Truong Cong Quynh

paper

Modules close to SSP- and SIP-modules

arXiv:1609.06788

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 $R_{R}$ 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 $C 2$ module.