Abstarct: A ring R is called a left Ikeda-Nakayama ring (left IN-ring) if the right annihilator of the intersection of any two left ideals is the sum of the two right annihilators. As a generalization of left IN-rings, a ring R is called a right SA-ring if the sum of right annihilators of two ideals is a right annihilator of an ideal of R. It would be interesting to find conditions under which the Ore extension R[x; α,δ], skew Laurent R[x,x-1; α], skew power series R[[x; α]] and skew Laurent series extensions R[[x, x−1; α]], is IN and SA. The purpose of this thesis is to study the behavior of the IN and SA property with respect to the Ore, skew Laurent, skew power series and skew Laurent series extensions. Furthermore, examples are provided to illustrate that the specified conditions are essential for the validity of the presented results. Without these conditions, the results would typically lose their validity.