International Journal of Engineering, Science and Mathematics

In this paper we investigate the following conditions.

(i) xy = (xy)^n(x,y)

(ii) xy = (xy)^n(x,y)

(iii) xy = y^m(x,y)x^n(x,y)

(iv) xy = xy^n(x,y)x

(v) xy = x^n(x,y)y^m(x,y) and finally prove that under appropriate additional hypothesis a d - g near ring must be commutative ring. The Theorem proved here is generalization of many recently established results.