Open AccessA note on almost prime submodule of CSM module over principal ideal domain
Author(s) -
I Gede Adhitya Wisnu Wardhana,
Nguyen Dang Hoa Nghiem,
Ni Wayan Switrayni,
Qurrotul Aini
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2106/1/012011
Subject(s) - associated prime , prime ideal , mathematics , prime (order theory) , minimal ideal , ideal (ethics) , prime element , annihilator , principal ideal , generalization , pure mathematics , ring (chemistry) , discrete mathematics , maximal ideal , algebra over a field , combinatorics , law , organic chemistry , political science , mathematical analysis , chemistry
An almost prime submodule is a generalization of prime submodule introduced in 2011 by Khashan. This algebraic structure was brought from an algebraic structure in ring theory, prime ideal, and almost prime ideal. This paper aims to construct similar properties of prime ideal and almost prime ideal from ring theory to module theory. The problem that we want to eliminate is the multiplication operation, which is missing in module theory. We use the definition of module annihilator to bridge the gap. This article gives some properties of the prime submodule and almost prime submodule of CMS module over a principal ideal domain. A CSM module is a module that every cyclic submodule. One of the results is that the idempotent submodule is an almost prime submodule.