International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 10836, 5 pages
doi:10.1155/2007/10836
Research Article
A Note on ⊕-Cofinitely Supplemented Modules
Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, China
Received 9 January 2007; Accepted 2 May 2007
Academic Editor: Francois Goichot
Copyright © 2007 Yongduo Wang and Qing Sun. 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.
Abstract
Let R be a ring and M a right R-module. In this note, we show that a quotient of an ⊕-cofinitely supplemented module is not in general ⊕-cofinitely supplemented and prove that if a module M is an ⊕-cofinitely supplemented multiplication module with Rad(M)≪M, then M can be written as an irredundant sum of local direct summand of M. An extension of the result of Calisici and Pancar [1], here it is shown that an arbitrary module is cofinitely semiperfect if and only if it is an (amply) cofinitely supplemented by supplements which have projective covers.