A ring R is called a right Ikeda-Nakayama ring (right IN -ring) if the left annihilator of the intersection of any two right ideals is the sum of two left annihilators. In this paper we show that if R is a right IN -rings and A and B are right ideals of R that are complements of each other, there exists an idempotent e in R such that A=e R and B = (1-e) R . As a consequence we show that R is right self injective if and only if (R) is a right IN -ring . Ring R is called dual ring ( D -ring) if every right or left ideal of R is an annihilator. It shown that R is a D -ring if and only if R is a left and right IN -ring and the dual of every simple right R -module is simple. Also, it will proved that R is quasi -Frobenius if and only if R is a left perfect, left and right IN -ring.