• Bulletin of the Korean Mathematical Society
• /
• v.56 no.2
• /
• pp.505-514
• /
• 2019

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.