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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)
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