Abstract
Let R be a prime ring with center [Formula: see text], δ: R → R a nonzero skew derivation, and n a fixed positive integer. In this paper, we show that R is a commutative ring if (i) [δ([x,y]),[x,y]]n = 0 for all x, y ∈ R or (ii) [Formula: see text] for all x ∈ R, except some specific cases.
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