Soft Union Ring and its Applications to Ring Theory
In this paper, soft union ring (SU ring) on a soft set is defined by using union operation of sets. This new concept shows how a soft set effects on a ring structure in the mean of union and inclusion of sets and from this overview, it functions as a bridge among soft set theory, set theory and ring theory. Then, its basic properties are derived and the relationship between soft intersection ring defined in [N. Cagman and F. Citak and H. Aktas, Soft intrings and its algebraic applications, Journal of Intelligent and Fuzzy Systems, 28 (3) 1225 1233 (2015) and SU ring are investigated. Furthermore, we give the applications of SU ring to ring theory.