Soft normed rings

This thesis consists of five sections. The introduction and a brief history of the titles in our study is given in the first section. Second section comprises basic definitions and theorems used in this thesis. In this section, there are the definitions of soft sets and normed rings. In the third section, we define soft normed rings through soft norms and we examine the ideals of soft normed rings, maximal soft ideals, the extension of maximal soft normed rings and the generalization of soft normed rings and also some algebraic structures on these topics are studied. In the fourth section, we define norms on quotient rings and on some algebraic structures which are not vector spaces. In addition, we study the algebraic and topological structure of these norms. Then these structures are defined on soft set theory, a wider theory in mathematics, and some basic properties are examined. The fifth and last section of this thesis is allocated to the results acquired during our study.