Journal of Mathematics and Statistics | |
Modules in σ[M] with Chain Conditions on δM-small Submodules | Science Publications | |
Ali O. Alattass1  | |
关键词: Small submodules; supplement submodules; chain conditions; M-singular; supplemented module; finitely generated; uniform dimension; nonzero submodules; positive integer; | |
DOI : 10.3844/jmssp.2011.144.148 | |
学科分类:社会科学、人文和艺术(综合) | |
来源: Science Publications | |
【 摘 要 】
Problem statement: Let M be a right module over a ring R. In this article modules in σ[M]with chain conditions on δM- small submodules are studied. Approach: With the help of knownresults about M- singular, Artinian and Noetherian modules the techniques of the proofs of our mainresults use the properties of δM- small, δM- supplement and δM- semimaximal submodules. Results:Modules in σ[M] with chain conditions on δM- small are investigated, δM- semimaximal submodule isdefined . Some Properties ofδM- semimaximal submodules are proved. As application a newcharacterization of Artinian module in σ[M] is obtained in terms of δM- small submodules and δM- semimaximalsubmodules, as well as δM- small submodules and δM- supplement submodules.Conclusion/Recommendations: Our results certainly generalized several results obtained earlier.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
---|---|---|---|
RO201912010160543ZK.pdf | 77KB | download |