On Armendariz rings

In this work, we studied relationship between Armendariz rings and the related rings. The study consists of four chapters. In the first chapter, we present some definations and theorems that will be used in the following chapters. In the second chapter, Baer and p.p.-rings were examined on polynomial rings which are related with Armendariz rings and examples were given for non Armendariz rings. ?A ring R is Armendariz if and only if polynomial ring R[x] is Armendariz? were shown . In addition Armendariz property on matrix rings, were examined . In the third chapter, polynomial rings on Armendariz rings were studied, moreover the relationships between semicommutativy and Armendariz property with semicommutative rings, were shown . Furthermore, extentions on Armendariz rings were investigated . In the last chapter, we studied abelian rings and its relations with the Armendariz rings are examined .