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.
"Applications of Soft Union Sets in the Ring Theory." J. Appl. Math. 2013 1 - 9, 2013. https://doi.org/10.1155/2013/474890