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 orderto provide these soft algebraic structures, the notion of λ,μ-soft union rings which is a generalization of that of soft union ringsis proposed. By introducing the notion of soft cosets, soft quotient rings based on λ,μ-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 λ,μ-soft union rings related to invariant soft sets are discussed