Modules in σ[M] with Chain Conditions on δM-small Submodules | Science Publications

Journal of Mathematics and Statistics

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 δ_M- 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 δ_M- small, δ_M- supplement and δ_M- semimaximal submodules. Results:Modules in σ[M] with chain conditions on δM- small are investigated, δ_M- 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 δ_M- small submodules and δ_M- semimaximalsubmodules, as well as δ_M- small submodules and δ_M- supplement submodules.Conclusion/Recommendations: Our results certainly generalized several results obtained earlier.

【 授权许可】

Unknown