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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Commuting and centralizing mappings in prime rings
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by J. Vukman PDF
Proc. Amer. Math. Soc. 109 (1990), 47-52 Request permission

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
  • © 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