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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On compositions of derivations of prime rings


Author: Chen-Lian Chuang
Journal: Proc. Amer. Math. Soc. 108 (1990), 647-652
MSC: Primary 16A72; Secondary 16A12
MathSciNet review: 998732
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Abstract: Let $ R$ be a prime ring and $ \varphi \left( {{x_i}} \right)$ be a differential polynomial of $ R$. It is shown that if $ \varphi \left( {{x_i}} \right) = 0$ holds on a nonzero two-sided ideal of $ R$, then $ \varphi \left( {{x_i}} \right) = 0$ holds on $ {R_F}$, the left Martindale quotient ring of $ R$. Using this together with Kharchenko's theorem on differential identities, we settle three problems raised by Krempa and Matczuk in the positive.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-0998732-3
PII: S 0002-9939(1990)0998732-3
Keywords: Prime rings, derivations, differential identities
Article copyright: © Copyright 1990 American Mathematical Society