Abstarct: Insertion-of-factors-property, which was introduced by Bell, has a role in the study of various sorts of zero-divisors in noncommutative rings. After the preliminary definitions, in chapter 2,we concern the structures of Armendariz rings and semicommutative rings which are generalizations of reduced rings, the polynomial rings over semicommutative rings, and the relationships between Armendariz rings and semicommutative rings. In chapter 3, we continue the study of reversible rings by Cohn. We first consider properties and basic extensions of reversible rings and related concepts to reversible rings, including some kinds of examples needed in the process. We next show that polynomial rings over reversible rings need not to be reversible, and sequentially argue about the reversibility of some kinds of polynomial rings. In chapter 4 and 5, We in this note consider this property in the case that factors are restricted to maximal ideals. A ring is called IMIP when it satisfies such property. It is shown that the Dorroh extension of A by K is an IMIP ring if and only if A is an IFP ring without identity, where A is a nil algebra over a field K. The structure of an IMIP ring is studied in relation to varsioun kinds of rings which have roles in noncommutative ring theory.