Nhảy đến nội dung

On 2-Primal Modules

Authors: 

Nguyen T. Bac, Hai Q. Dinh* and N.J. Groenewald

Source title: 
Thai Journal of Mathematics, 16(2), 2018 (Scopus)
Academic year of acceptance: 
2018-2019
Abstract: 

In this paper, the concept of $2$-primal modules is introduced. We show that the implications between rings which are reduced, IFP, symmetric and $2$-primal are preserved whenthe notions are extended to modules. Like for rings, for $2$-primal modules, prime submodules coincide with completely prime submodules. We prove that if$M$ is a quasi-projective and finitely generated right $R$-module which is a self-generator, then $M$ is $2$-primal if and only if $S =$End$_{R}(M$) is $2$-primal. Some properties of $2$-primal modules are also investigated.