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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
References
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 108 (1990), 31-37
  • MSC: Primary 16A72; Secondary 16A12, 16A68
  • DOI: https://doi.org/10.1090/S0002-9939-1990-0984803-4
  • MathSciNet review: 984803