TY  - JOUR
AU  - Alattass, Ali O. 
PY  - 2011
TI  - Modules in σ[M] with Chain Conditions on δM-small Submodules
JF  - Journal of Mathematics and Statistics
VL  - 7
IS  - 2
DO  - 10.3844/jmssp.2011.144.148
UR  - https://thescipub.com/abstract/jmssp.2011.144.148
AB  - 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 known results about M- singular, Artinian and Noetherian modules the techniques of the proofs of our main results 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 is defined. Some Properties of δM- semimaximal submodules are proved. As application a new characterization of Artinian module in σ[M] is obtained in terms of δM- small submodules and δM- semimaximal submodules, as well as δM- small submodules and δM- supplement submodules. Conclusion/Recommendations: Our results certainly generalized several results obtained earlier.