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Commuting and centralizing mappings in prime rings. (English) Zbl 0697.16035
The author proves a local version of a well known result of E. C. Posner [Proc. Am. Math. Soc. 8, 1093-1100 (1958; Zbl 0082.03003)] on centralizing derivations of prime rings. Let $$R$$ be a prime ring and $$D$$ a derivation of $$R$$. The main result of the paper is that if $$\text{char\,}R\neq 2,3$$, and if for all $$x\in R$$, $$[[D(x),x],x]=0$$, then either $$D=0$$ or $$R$$ is commutative.
Reviewer: C.Lanski

##### MSC:
 16W20 Automorphisms and endomorphisms 16N60 Prime and semiprime associative rings 16U70 Center, normalizer (invariant elements) (associative rings and algebras)
##### Keywords:
centralizing derivations; prime rings
Full Text:
##### References:
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