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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On nilpotent derivations of prime rings


Author: Chen-Lian Chuang
Journal: Proc. Amer. Math. Soc. 107 (1989), 67-71
MSC: Primary 16A72
DOI: https://doi.org/10.1090/S0002-9939-1989-0979224-6
MathSciNet review: 979224
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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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DOI: https://doi.org/10.1090/S0002-9939-1989-0979224-6
Keywords: Prime rings, Lie ideals, derivations, differential identities
Article copyright: © Copyright 1989 American Mathematical Society