On nilpotent derivations of prime rings

Chuang, Chen-Lian

doi:10.1090/S0002-9939-1989-0979224-6

On nilpotent derivations of prime rings
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Proc. Amer. Math. Soc. 107 (1989), 67-71 Request permission

Abstract:

Let $R$ be a prime ring with center $Z$ and let $U$ be a noncentral Lie ideal of $R$. Suppose that $d$ is a derivation of $R$ such that ${d^n}(u) \in Z$ for all $u \in U$, where $n$ is a fixed integer. It is shown that either ${d^n}(R) = 0$ or $R$ is an order of a $4$-dimensional simple algebra over a field of characteristic 2.

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