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An Engel condition with derivation


Author: Charles Lanski
Journal: Proc. Amer. Math. Soc. 118 (1993), 731-734
MSC: Primary 16W25; Secondary 16N60
DOI: https://doi.org/10.1090/S0002-9939-1993-1132851-9
MathSciNet review: 1132851
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Abstract: Let $ R$ be a prime ring, $ L$ a noncommutative Lie ideal of $ R$, and $ D$ a nonzero derivation of $ R$. If for each $ x \in L$, $ {[D(x),x]_k} = [[ \cdots [D(x),x],x], \ldots ,x] = 0$ with $ k$ fixed, then $ \operatorname{char} (R) = 2$ and $ R \subseteq {M_2}(F)$ for $ F$ a field.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1132851-9
Article copyright: © Copyright 1993 American Mathematical Society

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