Affiliation:
1. Department of Mathematics, College of Sciences, Shiraz University, Shiraz 71454, Iran
Abstract
Let M be an R-module. If for every submodule N of M, there exists an element r ∈ R such that N=rM, then we say that M is a principal ideal multiplication module. In this paper, the relations between principal ideal multiplication modules, multiplication modules, cyclic modules, and modules over principal ideal rings are studied. It is proved that every principal ideal multiplication module over any quotient of a Dedekind domain is cyclic. Also, every principal ideal multiplication module with prime annihilator ideal is cyclic.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Algebra and Number Theory
Cited by
7 articles.
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1. Strong -Submodules of a Module;Journal of Mathematics;2023-03-24
2. S-principal ideal multiplication modules;Communications in Algebra;2023-01-11
3. On Principal Ideal Multiplication Modules;Ukrainian Mathematical Journal;2017-08
4. A Prime Submodule Principle;Algebra Colloquium;2014-10-06
5. A Note on Comultiplication Modules;Algebra Colloquium;2014-01-20