Table of Contents
ISRN Algebra
Volume 2014, Article ID 603851, 4 pages
http://dx.doi.org/10.1155/2014/603851
Research Article

Generalized -Radical Supplemented Modules

1Faculty of Art and Science, Amasya University, İpekköy, 05100 Amasya, Turkey
2Department of Mathematics, Faculty of Art and Science, Ondokuz Mayis University, Kurupelit, 55139 Samsun, Turkey

Received 28 October 2013; Accepted 16 December 2013; Published 14 January 2014

Academic Editors: A. V. Kelarev and S. Yang

Copyright © 2014 Burcu Nişancı Türkmen and Ali Pancar. 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

Çalışıcı and Türkmen called a module generalized -supplemented if every submodule has a generalized supplement that is a direct summand of . Motivated by this, it is natural to introduce another notion that we called generalized -radical supplemented modules as a proper generalization of generalized -supplemented modules. In this paper, we obtain various properties of generalized -radical supplemented modules. We show that the class of generalized -radical supplemented modules is closed under finite direct sums. We attain that over a Dedekind domain a module is generalized -radical supplemented if and only if is generalized -radical supplemented. We completely determine the structure of these modules over left -rings. Moreover, we characterize semiperfect rings via generalized -radical supplemented modules.