Journal of Mathematics and Statistics

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

Ali O. Alattass

DOI : 10.3844/jmssp.2011.144.148

Journal of Mathematics and Statistics

Volume 7, Issue 2

Pages 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.

Copyright

© 2011 Ali O. Alattass. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.