On Soft Ring and Soft Topological Ring

Abstract

Soft set theory is an affective mathematical tool to solve problems that involves uncertainties. Despite the development in the theoretical structure of soft sets, researchers did not make consensus formulation of soft element. In this study soft ring is redefined by the help of soft operation which are based on a natural definition of soft element. This new soft ring definition is compared with the soft ring definition in the literature. Some examples, results and theorems are given to enrich the concept of soft ring. Also soft topological ring structure which is a harmonization of soft ring and soft topology is studied with some results.