Construction and characteristics of soft union rings and right and left ideals of soft union rings

Many mathematical structures have been characterized by Soft Set Theory, proposed by Molodtsov, for modelling uncertainty in time. In this thesis, by applying soft set theory to rings, we construct soft union rings and ideals and study their properties. First, some definitions regarding soft sets and some algebraic structures are given. Then, soft union rings, soft union right (left) ideals of rings are defined and their basic properties are obtained by using soft set operations. The relation of soft union rings and ideals with the soft intersection-union product definition, defined on the soft sets the parameter set of which are rings, are given. Finallay, regular rings are characterized via soft union ideals of rings.