International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 58132, 8 pages
-Small Submodules and -Supplemented Modules
Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, China
Received 9 January 2007; Accepted 18 June 2007
Academic Editor: Akbar Rhemtulla
Copyright © 2007 Yongduo Wang. 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 ring and a
right -module. It is shown that (1) is Noetherian if and only if satisfies ACC on -small submodules; (2) is Artinian if and only if satisfies DCC on
-small submodules; (3) is Artinian if and only if is
an amply -supplemented module and satisfies DCC on
-supplement submodules and on -small submodules.