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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.