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http://dx.doi.org/10.4134/BKMS.b180382

A NOTE ON MONOFORM MODULES

Hajikarimi, Alireza (Mobarakeh Branch Islamic Azad University)
Naghipour, Ali Reza (Department of Mathematical Sciences Shahrekord University)

Publication Information

Bulletin of the Korean Mathematical Society / v.56, no.2, 2019 , pp. 505-514 More about this Journal

Abstract

Let R be a commutative ring with identity and M be a unitary R-module. A submodule N of M is called a dense submodule if $Hom_R(M/N,\;E_R(M))=0$ , where $E_R(M)$ is the injective hull of M. The R-module M is said to be monoform if any nonzero submodule of M is a dense submodule. In this paper, among the other results, it is shown that any kind of the following module is monoform. (1) The prime R-module M such that for any nonzero submodule N of M, $Ann_R(M/N){\neq}Ann_R(M)$ . (2) Strongly prime R-module. (3) Faithful multiplication module over an integral domain.

Keywords

dense submodule; prime module; monoform module; injective hull; multiplication module;

Citations & Related Records

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