• Published : 2005.11.01


Let R be a noncommutative semi prime ring. Suppose that there exists a derivation d : R $\to$ R such that for all x $\in$ R, either [[d(x),x], d(x)] = 0 or $\langle$$\langle(x),\;x\rangle,\;d(x)\rangle$ = 0. In this case [d(x), x] is nilpotent for all x $\in$ R. We also apply the above results to a Banach algebra theory.


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