Applications of soft union sets in the ring theory

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. © 2013 yongwei yang et al.