Derivations with nilpotent values on Lie ideals

Lanski, Charles

doi:10.1090/S0002-9939-1990-0984803-4

Derivations with nilpotent values on Lie ideals
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by Charles Lanski PDF

Proc. Amer. Math. Soc. 108 (1990), 31-37 Request permission

Abstract:

Let $R$ be a ring containing no nonzero nil right ideal and let $U$ be a Lie ideal of $R$. If $d$ is a derivation of $R$ so that $d(u)$ is a nilpotent element for each $u \in U$, then $d = 0$ when $R$ is a prime ring and $U$ is not commutative. The main result shows that in general, $d(I) = 0$ for $I$ the ideal $R$ generated by $[U,U]$ and that $R$ is the subdirect sum of two images so that $d$ induces the zero derivation on one, and the image of $U$ in the other is commutative.

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