Boolean near rings and Boolean ideals

This thesis consists of four sections. In the first section, the literature knowledge about the study has been given. Basic knowledges about the near rings and Boolean rings have been given detailed in the second and thirth section, respectively. In the fourth section, which consists of an original study, the concept of Boolean near ring extended to ideals of near-rings, called Boolean ideals. With the obtained new concept the relationships between Boolean ideals and the other concepts in the literature have been examined. It has been proved that a Boolean ideal is also an IFP ideal but the converse is not true. Some relationships between prime ideals and Boolean ideals in near-rings have been obtained. Also, it has been proved that annihilator ideals of Boolean near-rings are also Boolean ideals. Moreover it has been examined but that some examples to illustrate some near rings, which is not a Boolean near-ring, have Boolean ideals. Finally, a Boolean near ring has been obtained from a given Boolean ring through the method of obtaining a Boolean near ring. Keywords: Near ring, Boolean ring, Boolean near ring, Boolean ideal, IFP ideal.