Abstract
Let $R$ be a prime ring without nonzero nil one-sided ideals. Suppose that $g$ is a generalized derivation of $R$ and that $f(X_{1},\cdots,X_{k})$ is a multilinear polynomial not central-valued on $R$ such that $g(f(x_{1},\cdots,x_{k}))$ is nilpotent for all $x_{1},\cdots,x_{k}$ in some nonzero ideal of $R$. Then $g=0$.
Citation
Jer-Shyong Lin. Cheng-Kai Liu. "GENERALIZED DERIVATIONS WITH NILPOTENT VALUES ON MULTILINEAR POLYNOMIALS." Taiwanese J. Math. 10 (5) 1183 - 1192, 2006. https://doi.org/10.11650/twjm/1500557297
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