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The Scientific World Journal
Volume 2014 (2014), Article ID 541630, 9 pages
http://dx.doi.org/10.1155/2014/541630
Research Article

Soft Congruence Relations over Rings

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

Received 25 February 2014; Accepted 1 April 2014; Published 24 April 2014

Academic Editor: Feng Feng

Copyright © 2014 Xiaolong Xin and Wenting Li. 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

Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainty. In this paper, we initiate the study of soft congruence relations by using the soft set theory. The notions of soft quotient rings, generalized soft ideals and generalized soft quotient rings, are introduced, and several related properties are investigated. Also, we obtain a one-to-one correspondence between soft congruence relations and idealistic soft rings and a one-to-one correspondence between soft congruence relations and soft ideals. In particular, the first, second, and third soft isomorphism theorems are established, respectively.