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On the structure of semiderivations in prime rings


Author: Chen-Lian Chuang
Journal: Proc. Amer. Math. Soc. 108 (1990), 867-869
MSC: Primary 16A72
DOI: https://doi.org/10.1090/S0002-9939-1990-1002154-9
MathSciNet review: 1002154
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Abstract: Let $ R$ be a prime ring. By a semiderivation associated with a function $ g:R \to R$, we mean an additive mapping $ f:R \to R$ such that, for all $ x,y \in R,f(xy) = f(x)g(y) + xf(y) = f(x)y + g(x)f(y)$ and $ f(g(x)) = g(f(x))$. It is known that $ g$ must necessarily be a ring endomorphism. Here it is shown that $ f$ must be an ordinary derivation or of the form $ f(x) = \lambda (x - g(x))$ for all $ x \in R$, where $ \lambda $ is an element of the extended centroid of $ R$.


References [Enhancements On Off] (What's this?)

  • [1] H. E. Bell and W. S. Martindale, III, Semiderivations and commutativity in prime rings, Canad. Math. Bull. 31 (4) (1988), 500-508. MR 971579 (89k:16063)
  • [2] J. Bergen, Derivations in prime rings, Canad. Math. Bull. 26 (1983), 267-270. MR 703394 (85a:16019)
  • [3] J.-C. Chang, On semiderivations of prime rings, Chinese J. Math. 12 (1984), 255-262. MR 774289 (86g:16050)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1002154-9
Keywords: Semiderivation, derivation, endomorphism, extended centroid
Article copyright: © Copyright 1990 American Mathematical Society

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