On the uniqueness of almost prime submodules within cyclic uniserial modules

Wardhana, I Gede Adhitya Wisnu; Maulana, Fariz; Sarmin, Nor Haniza

doi:10.47974/JDMSC-2194

Open Access Research Article

On the uniqueness of almost prime submodules within cyclic uniserial modules

^*I Gede Adhitya Wisnu WardhanaCorresponding authoradhitya.wardhana@unram.ac.idDepartment of Mathematics Faculty of Mathematics and Natural Sciences Universitas MataramMataram, IndonesiaView full profile → , Fariz Maulanafarizholmes@gmail.comDepartment of Mathematics Faculty of Mathematics and Natural Sciences Universitas MataramMataram, IndonesiaView full profile → , Nor Haniza Sarminnhs@utm.myDepartment of Mathematical Sciences Faculty of Sciences Universiti Teknologi MalaysiaJohor, MalaysiaView full profile →

* Corresponding author · click or hover a name for details

pp. 239–247Vol. 28Issue 1February 2025DOI: 10.47974/JDMSC-2194 Crossmark XML

Received:: 06 Mar 2024
Published Online:: 28 Feb 2025
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2194
Pages:: 239–247

Abstract

A uniserial module is a module that satisfies both ascending chain condition and descending chain condition, which makes a uniserial module an Artinian module and a Noetherian module at the same time. Recently an algebraic structure from ring theory, called almost prime ideal, is generalized into a module theory and called an almost prime submodule. Some researchers have examined the characterizations of this new algebraic structure in various types of modules. In this article, we provide some insights into the almost prime submodule of a uniserial cyclic module In this study, we have discovered that the non-zero almost prime submodule of the cyclic uniserial module is unique.

Keywords

Almost prime submodule Cyclic uniserial module Principal ideal domain

Subject Classifications

13C0513C1013C12

References

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