On 2-Primal Modules

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

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 when the 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 =EndR(M) is 2-primal. Some properties of 2-primal modules are also investigated.