ISRN Discrete Mathematics
Volume 2011 (2011), Article ID 939687, 5 pages
Notes on the Union of Weakly Primary Submodules
Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran
Received 30 August 2011; Accepted 18 October 2011
Academic Editor: U. A. Rozikov
Copyright © 2011 Peyman Ghiasvand and Farkhonde Farzalipour. 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.
Let be a commutative ring with identity, and let be an -module. A proper submodule of is said to be weakly primary if for and , which implies that either or for some positive integer . In this paper, we study weakly primary submodules, and we investigate the union of weakly primary submodules of -modules.