Let R be a 2-torsion free semiprime ring, I a nonzero ideal of R, Z the center of R and D:R ⊿ ＊R a derivation. If d[x,y]+[x,y] ⊿ Z or d[x,y] ⊿ ＊[x,y] ⊿ Z for all x, y ⊿ I, then R is commutative.
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