A generalization of reduced rings

This thesis consist of abstract, basic concepts, introduction and three main chapters. The first main section is Quasi-reduced rings, the second main section is A generalization of reduced rings, and the third main section is Rings in which every nilpotent is central. A ring R is usually called reduced if for a∈R, a^2=0 implies a=0. This thesis is concerned with a generalization of reduced rings. A ring R central rigid if for a,b∈R, a^2 b=0 implies that ab=0 is central. Thesis contains sufficient conditions for central rigid rings to be reduced. A ring R is Quasi-reduced if for a,b∈R,ab = 0 implies that (aR) ∩ (Rb) ⊆ C(R). Thesis is divided Quasi-reduced rings as a generalization of reduced rings. It is contained basic properties of Quasi-reduced rings are establish-among them, the structure of such rings and their extensions.