Leavitt path algebras with coefficients in commutative ring

In this thesis, Leavitt path algebras with coefficients in a commutative ring are examined and the multiplicative properties of the ideals in Leavitt path algebras are given. The first two chapters of this thesis which is of five chapters consists of the history of Leavitt path algebras and the definitions and notions in ring and module theory. The third chapter of this thesis contains the definitions and theorems related to Leavitt path algebras L_K(E) with coefficients in a field K and Leavitt path algebras L_R(E) with coefficients in a unital commutative ring R. In the fourth chapter which is the original part of the thesis, the multiplicative properties of the ideals in Leavitt path algebra L_R(E) are mentioned and it is proved that Leavitt path algebra L_R(E) is an arithmetical ring. In the last chapter, some problems that will give direction for the next study are given for researchers interested in Leavitt path algebras L_R(E).