1. TASLEEM LAL - Department of Mathematics, Khwaja Fareed University of Engineering and Information Technology,
Pakistan.

2. ZAHEER AHMAD - Department of Mathematics, Khwaja Fareed University of Engineering and Information Technology,
Pakistan.

3. MUHAMMAD HAMZA - Department of Mathematics, Khwaja Fareed University of Engineering and Information Technology,
Pakistan.

4. UMBER RANA - Department of Mathematics, Khwaja Fareed University of Engineering and Information Technology,
Pakistan.

5. MUNTAZIM ABBAS - Department of Mathematics, Khwaja Fareed University of Engineering and Information Technology,
Pakistan.

6. MOHSIN BILAL - Department of Mathematics, Khwaja Fareed University of Engineering and Information Technology,
Pakistan.

In this paper, the commutativity of quotient Γ-ring has been proved. In this article by applying some algebraic technique (i) [D1(x1), D2(y1)]α – [x1, y1]α ∈P1 (ii) (D1(x1)o D2(y1))α-(x1 oy1)α∈ P1 (iii) [D1(x1), D2(y1)]α-(x1 oy1)α∈P1 (iv) (D1(x1)o D2(y1))α- [x1, y1]α∈P1 ,for all x1, y1∈M, and α∈Γ. Where M be an arbitrary Γ-ring and P1 be a prime ideal. Mainly, the relation between the behavior of Γ-derivation and the structure of this class of Γ-ring has been established.

Integral Domain, Prime ideals, Γ-ring