sigma-Ideals and Generalized Derivations in sigma-Prime Rings

Let R be a sigma-prime ring and F and G be generalized derivations of R, wiassociatedth derivations d and g respectively. In the present paper; we shall investigate the comroutativity of R admitting generalized derivations F and G satisfying any one of the properties: (i) F(x)y+F(y)x = xG(y)+yG(x), (ii) F(x(2)) x(2), (iii) [F(x), y] = [x, G(y)], (iv) d(x)F(y) = xy, (v) F (x,y]) = [F(x), Y] + [d(y), x] and (vi) F(x o y) - F(x) o y - d(y) o x for ail x, y in some appropriate subset of R.