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Proceedings of the American Mathematical Society

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



Semiderivations of prime rings

Author: Matej Brešar
Journal: Proc. Amer. Math. Soc. 108 (1990), 859-860
MSC: Primary 16A72; Secondary 16A12
MathSciNet review: 1007488
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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.

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Keywords: Semiderivation, derivation, endomorphism, prime ring, extended centroid
Article copyright: © Copyright 1990 American Mathematical Society

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