Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1990-0984803-4
MathSciNet review: 984803
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A72, 16A12, 16A68

Retrieve articles in all journals with MSC: 16A72, 16A12, 16A68


Additional Information

Article copyright: © Copyright 1990 American Mathematical Society