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

Commuting and centralizing mappings in prime rings


Author: J. Vukman
Journal: Proc. Amer. Math. Soc. 109 (1990), 47-52
MSC: Primary 16A12; Secondary 16A68, 16A72
MathSciNet review: 1007517
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Abstract: Let $ R$ be a ring. A mapping $ F:R \to R$ is said to be commuting on $ R$ if $ [F(x),x] = 0$ holds for all $ x \in R$. The main purpose of this paper is to prove the following result, which generalizes a classical result of E. Posner: Let $ R$ be a prime ring of characteristic not two. Suppose there exists a nonzero derivation $ D:R \to R$, such that the mapping $ x \mapsto [D(x),x]$ is commuting on $ R$. In this case $ R$ is commutative.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1007517-3
PII: S 0002-9939(1990)1007517-3
Keywords: Prime ring, derivation, Jordan derivation, inner derivation, commuting mapping, centralizing mapping
Article copyright: © Copyright 1990 American Mathematical Society