A NOTE ON MONOFORM MODULES
Bull. Korean Math. Soc.
Published online 2019 Mar 13
Alireza Hajikarimi, and Alireza Naghipour
Department of Mathematical Sciences, Shahrekord University, Mobarakeh Branch, Islamic Azad University
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) is not equal to
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
MSC numbers : 2010 Mathematics Subject Classification: 13C05, 13C11, 13E05
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