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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 in prime rings

Author: B. Felzenszwalb
Journal: Proc. Amer. Math. Soc. 84 (1982), 16-20
MSC: Primary 16A72; Secondary 16A12
MathSciNet review: 633268
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Abstract: Let $ R$ be a ring and $ d \ne 0$ a derivation of $ R$ such that $ d({x^n}) = 0$, $ n = n(x) \geqslant 1$, for all $ x \in R$. It is shown that if $ R$ is primitive then $ R$ is an infinite field of characteristic $ p > 0$ and $ p\vert n(x)$ if $ d(x) \ne 0$. Moreover, if $ R$ is prime and the set of integers $ n(x)$ is bounded, the same conclusion holds.

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PII: S 0002-9939(1982)0633268-6
Article copyright: © Copyright 1982 American Mathematical Society