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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Derivations with nilpotent values on Lie ideals


Author: Charles Lanski
Journal: Proc. Amer. Math. Soc. 108 (1990), 31-37
MSC: Primary 16A72; Secondary 16A12, 16A68
MathSciNet review: 984803
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1990-0984803-4
PII: S 0002-9939(1990)0984803-4
Article copyright: © Copyright 1990 American Mathematical Society