Abstract
Let R be a prime ring, I a nonzero ideal of R, d a derivation of R and m, n fixed positive integers. (i) If (d[x, y])m = [x, y] n for all x, y ∈ I, then R is commutative. (ii) If Char R ≠ 2 and [d(x), d(y)] m = [x, y]n for all x, y ∈ I, then R is commutative. Moreover, we also examine the case when R is a semiprime ring.
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Huang, S. Derivations with engel conditions in prime and semiprime rings. Czech Math J 61, 1135–1140 (2011). https://doi.org/10.1007/s10587-011-0053-7
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DOI: https://doi.org/10.1007/s10587-011-0053-7