On the structure of semiderivations in prime rings
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- by Chen-Lian Chuang
- Proc. Amer. Math. Soc. 108 (1990), 867-869
- DOI: https://doi.org/10.1090/S0002-9939-1990-1002154-9
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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
- H. E. Bell and W. S. Martindale III, Semiderivations and commutativity in prime rings, Canad. Math. Bull. 31 (1988), no. 4, 500–508. MR 971579, DOI 10.4153/CMB-1988-072-9
- Jeffrey Bergen, Derivations in prime rings, Canad. Math. Bull. 26 (1983), no. 3, 267–270. MR 703394, DOI 10.4153/CMB-1983-042-2
- Jui Chi Chang, On semiderivations of prime rings, Chinese J. Math. 12 (1984), no. 4, 255–262. MR 774289
Bibliographic Information
- © Copyright 1990 American Mathematical Society
- 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