Abstarct: This thesis first we examinning the exxpression of the IF P -rings and contains a nonzero nilpotent ideals. Also on Von Neumann regular rings are examine the conditions. So we show that 2-primal rings are locally 2-primal and locally 2-primal rings are NI rings but we show that there are NI rings which are not locally 2-primal. So we prove that every minimal noncommutative (locally) 2-primal ring is isomorphic to the 2 by 2 upper traingular matrix ring over GF(2). A nil ring R need not be locally 2-primal, but we show that it is the case if and only if R is a Levitzki radical ring. Fainally, the present note the structures of IF P rings and near-IF P rings are observed,extending the classes of them. We show that the near-IF P ness and the NIness are distinct each other and the relations among them and related conditions are examined.