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 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.

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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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|ISSN 1686-0209|