Applications of Soft Union Sets in the Ring Theory

الملخص EN

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 λ,μ-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 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.