A note on monoform modules
Bull. Korean Math. Soc. 2019 Vol. 56, No. 2, 505-514
https://doi.org/10.4134/BKMS.b180382
Published online March 1, 2019
Alireza Hajikarimi, Ali Reza Naghipour
Islamic Azad University; Monash 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 ${\rm{Hom}}_R(M/N,E_R(M))=0$, 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 $M$, ${\rm{Ann}}_R(M/N)\neq{\rm{Ann}}_R(M)$.
(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 : 13C05, 13C11, 13E05
Full-Text :

   

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd