**Thesis Type:** Postgraduate

**Institution Of The Thesis:** Marmara University, Institute for Graduate Studies in Pure and Applied Sciences, Department of Mathematics, Turkey

**Approval Date:** 2015

**Thesis Language:** Turkish

**Student:** SUAT KOÇ

**Supervisor: **Ünsal Tekir

In this study, the relations between z-ideals and z-filters of rings of continuous functions C(X) (or C) on any topological space X are given and also the distribution of prime ideals in C(X) is investigated. Furthermore, Let P be a prime ideal in C(X), then the primary ideals in residue class ring C/P are studied. Therefore, Firstly in the first section of the first chapter of this thesis, fundemantal definitions and some theorems that will be used in other chapters are given. Also in the second and other parts of the first chapter, algebraic and order structure of C(X) are studied. In the second chapter, the relations between topological properties of X and algebraic properties of C(X) are given. Moreover, the notion of 2-absorbing z-filter which is a generalization of prime z-filter is introduced and the relation between 2-absorbing z-ideal of C(X) and 2-absorbing z-filter on X is given. In the third chapter, order structure of residue class ring C/P and the distribution of prime ideals are investigated. Furthermore, it is shown that prime ideals containing a prime ideal P in C(X) form a chain and some theorems about prime z-ideals in C(X) are given. Finally, primary ideals of residue class ring C/P are charectarized and also it is shown that an ideal may not be the intersection of primary ideals in a general commutative ring |