Bipolar soft ideals of gamma near-rings

With the advancement of scientific studies, problems involving uncertainty have emerged. Classical mathematics was insufficient to model or make sense of these uncertain problems. Due to this insufficiency, scientists have put forward new theories. One of them is the soft set theory, which was first studied by Molodtsov. Then, many researchers have done various studies in different fields using soft sets. In this thesis, first of all, basic definitions and theorems about algebra were given. Afterward, gamma rings, near-rings, near-gamma-rings and soft sets are examined with definitions and theorems have been studied. In the second part, some bipolar soft structures such as bipolar soft sets, bipolar soft groups, and bipolar soft ideals in near-rings were investigated. In addition to this, bipolar soft ideals of a gamma near-ring were defined. Some basic properties of this algebraic structure have been analyzed. Bipolar soft coset set was defined with the help of bipolar soft ideals and this set was shown to be a gamma near ring. Finally, a function was defined with the help of bipolar soft ideals of a gamma near ring and this study was concluded by showing that this function is a gamma near-ring epimorphism.