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On a generalization of the notion of centralizing mappings


Author: Matej Brešar
Journal: Proc. Amer. Math. Soc. 114 (1992), 641-649
MSC: Primary 16U80; Secondary 16U70, 16W25
DOI: https://doi.org/10.1090/S0002-9939-1992-1072330-X
MathSciNet review: 1072330
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Abstract: Let $ R$ be a ring with center $ Z$. A mapping $ f:R \to R$ is called centralizing (resp. commuting) if $ [f(x),x] \in Z$ (resp. $ [f(x),x] = 0$) for all $ x \in R$. In this paper we consider a more general case where a mapping $ f:R \to R$ satisfies $ [[f(x),x],x] = 0$ for all $ x \in R$; it is shown that if $ R$ is a prime ring of characteristic not 2, then every additive mapping with this property is commuting.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1072330-X
Keywords: Centralizing mapping, commuting mapping, prime ring, extended centroid
Article copyright: © Copyright 1992 American Mathematical Society

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