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Journal of Applied Mathematics
Volume 2013, Article ID 474890, 9 pages
http://dx.doi.org/10.1155/2013/474890
Research Article

Applications of Soft Union Sets in the Ring Theory

Department of Mathematics, Northwest University, Xi'an 710127, China

Received 3 July 2013; Accepted 28 October 2013

Academic Editor: Zhihong Guan

Copyright © 2013 Yongwei Yang et al. 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

The aim of the paper is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notion of -soft union rings which is a generalization of that of soft union rings is proposed. By introducing the notion of soft cosets, soft quotient rings based on -soft union ideals are established. Moreover, through discussing quotient soft subsets, an approach for constructing quotient soft union rings is made. Finally, isomorphism theorems of -soft union rings related to invariant soft sets are discussed.