Commuting and centralizing mappings in prime rings
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- by J. Vukman
- Proc. Amer. Math. Soc. 109 (1990), 47-52
- DOI: https://doi.org/10.1090/S0002-9939-1990-1007517-3
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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.References
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Bibliographic Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 47-52
- MSC: Primary 16A12; Secondary 16A68, 16A72
- DOI: https://doi.org/10.1090/S0002-9939-1990-1007517-3
- MathSciNet review: 1007517