| Let R be a prime ring , d is a nonzero derivation of R, Z is the center of R, E-C Posner has shown:If [x, d(x)] G Z, ∨x G R, then R is commutative ring [5].Joseph H Mayne extended this result to x ∈ A, A is nonzero ideal of R [9].When chR ≠2,P.H.Lee and T.R.Lee has shown:V is Lie ideal of R ,5 too.b is a nonzero derivation of R. In [2],A.Ram has shown by example " It's not true when chR = 2[1]. When chR = 2,paper [7] has shown if R is not S4-ring and d2 ≠0δ2≠0When chR = 2,S be a nonzero adjoint ideal of R in [8] proved that1. If [5, d(5)] ∈Zthen R is commutative ring.2. If [d(5), d(S)) then R is commutative ring.3. If dδ(S) then R is commutative ring. |
