Modules close to SSP- and SIP-modules

Abyzov Adel; Tran Hoai Ngoc Nhan; Truong Cong Quynh

Modules close to SSP- and SIP-modules

Rings and Algebras 2016-10-14 v2

Authors: Abyzov Adel , Tran Hoai Ngoc Nhan , Truong Cong Quynh

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 $C2$ module.

Keywords

module theory commutative ring theory

Cite

@article{arxiv.1609.06788,
  title  = {Modules close to SSP- and SIP-modules},
  author = {Abyzov Adel and Tran Hoai Ngoc Nhan and Truong Cong Quynh},
  journal= {arXiv preprint arXiv:1609.06788},
  year   = {2016}
}

Modules close to SSP- and SIP-modules

Abstract

Keywords

Cite

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