Annihilator Condition on Power Values of Commutators with Derivations

摘要

Let R be a prime ring with center Z(R),I a nonzero ideal of R,d a nonzero derivation of R and 0 ≠ a ∈ R.In the present paper,our object is to study the situation a[d(xk),xk]n ∈ Z(R) for all x ∈ I under certain conditions,where n (≥ 1),k (≥ 1) are fixed integers.