Module structure over Leavitt path algebras

This thesis consists of five main chapters. In the first chapter, the introduction, the history of Leavitt path algebras is mentioned. The studies on Leavitt path algebras whose coefficients are taken from the K field and Leavitt path algebras whose coefficients are taken from the commutative ring R with unity are mentioned. Also, studies on the module structure of Leavitt path algebra are discussed. The second chapter is divided into two sub-titles as group, ring, module theory and graph theory. In these sub-titles, the main definitions, theorems and examples that we use in the following sections of the thesis are given. In the third chapter, the definition and examples of Leavitt path algebras, the coefficients of which are taken from the field K, are given, and the theorems that give the properties of Leavitt path algebras are mentioned. In the fourth chapter, which is the main part of the thesis, the theorems related to the module structure of Leavitt path algebras are examined in detail. In the last chapter, the f i fth chapter, conclusions and recommendations are given.