Semiderivations of prime rings
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- by Matej Brešar
- Proc. Amer. Math. Soc. 108 (1990), 859-860
- DOI: https://doi.org/10.1090/S0002-9939-1990-1007488-X
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Abstract:
A semiderivation of a ring $R$ is an additive mapping $f:R \to R$ together with a function $g:R \to R$ such that $f(xy) = f(x)g(y) + xf(y) = f(x)y + g(x)f(y)$ and $f(g(x)) = g(f(x))$ for all $x,y \in R$. We prove that the only semiderivations of prime rings are derivations and mappings of the form $f(x) = \lambda (x - g(x))$, where $g$ is an endomorphism and $\lambda$ is an element in the extended centroid.References
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Bibliographic Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 108 (1990), 859-860
- MSC: Primary 16A72; Secondary 16A12
- DOI: https://doi.org/10.1090/S0002-9939-1990-1007488-X
- MathSciNet review: 1007488