@article {10.3844/jmssp.2011.144.148,
article_type = {journal},
title = {Modules in σ[M] with Chain Conditions on δM-small Submodules},
author = {Alattass, Ali O.},
volume = {7},
year = {2011},
month = {May},
pages = {144-148},
doi = {10.3844/jmssp.2011.144.148},
url = {https://thescipub.com/abstract/jmssp.2011.144.148},
abstract = {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.},
journal = {Journal of Mathematics and Statistics},
publisher = {Science Publications}
}