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Journal of Applied Mathematics
Volume 2013, Article ID 630285, 7 pages
Research Article

-Regular Modules

1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
2Applied Science Department, University of Technology, Baghdad 10001, Iraq

Received 9 November 2012; Accepted 3 February 2013

Academic Editor: Jong Hae Kim

Copyright © 2013 Areej M. Abduldaim and Sheng Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We introduced and studied -regular modules as a generalization of -regular rings to modules as well as regular modules (in the sense of Fieldhouse). An -module is called -regular if for each and , there exist and a positive integer such that . The notion of -pure submodules was introduced to generalize pure submodules and proved that an -module is -regular if and only if every submodule of is -pure iff   is a -regular -module for each maximal ideal of . Many characterizations and properties of -regular modules were given. An -module is -regular iff is a -regular ring for each iff is a -regular ring for finitely generated module . If is a -regular module, then .