Applications of Soft Union Sets in the Ring Theory

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 $\left(\lambda ,\mu \right)$-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 $\left(\lambda ,\mu \right)$-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 $\left(\lambda ,\mu \right)$-soft union rings related to invariant soft sets are discussed.