In this paper we prove three results on semi-prime rings (i) If R is a 2-torsion free semi-prime ring satisfying [(xy)~2, [xy,yx]] = 0 for all x,y in R, then R is commutative, (ii) If R is a 2-torsion free semi-prime ring satisfying [xy~n, [xy, yx]] = 0 for all x, y in R, then R is commutative. (iii) If R is a 2-torsion free semi-prime ring satisfying [y~nx, [xy,yx]] = 0 for all x, y in R, then R is commutative.
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