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

 

Note on nilpotent derivations


Authors: P. H. Lee and T. K. Lee
Journal: Proc. Amer. Math. Soc. 98 (1986), 31-32
MSC: Primary 16A72; Secondary 16A70
MathSciNet review: 848869
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Abstract: Let $ R$ be a prime ring with center $ Z$. Suppose that $ d$ is a derivation on $ R$ such that $ {d^n}(x) \in Z$ for all $ x$, where $ n$ is a fixed integer. It is shown that either $ {d^n}(x) = 0$ for all $ x \in R$ or $ R$ is a commutative integral domain. Moreover, the same conclusion holds even if we assume that $ {d^n}(x) \in Z$ merely for all $ x \in I$, where $ I$ is a nonzero ideal of $ R$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0848869-3
PII: S 0002-9939(1986)0848869-3
Keywords: Prime rings, derivations
Article copyright: © Copyright 1986 American Mathematical Society