Some results on ?-ideal of ?-prime ring

Let R be a ?-prime ring with characteristic not 2, Z(R) be the center ofR, I be a nonzero ?-ideal of R, ?, ? : R -> R be two automorphisms, dbe a nonzero (?, ?)-derivation of R and h be a nonzero derivation of R.In the present paper, it is shown that (i) If d (I) ? C?,?and ? commuteswith ? then R is commutative. (ii) Let ? and ? commute with ?. Ifa ? I ? S?(R) and [d(I), a]and h commute with ?. If dh (I) ? C?,?and h (I) ? I then R is? C commutative.