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

 

Lie ideals and Jordan derivations of prime rings


Author: Ram Awtar
Journal: Proc. Amer. Math. Soc. 90 (1984), 9-14
MSC: Primary 16A72; Secondary 16A68
MathSciNet review: 722405
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Abstract: Herstein proved [1, Theorem 3.3] that any Jordan derivation of a prime ring of characteristic not 2 is a derivation of $ R$. Our purpose is to extend this result on Lie ideals. We prove the following

Theorem. Let $ R$ be any prime ring such that char $ R \ne 2$ ana let $ U$ be a Lie ideal of $ R$ such that $ {u^2} \in U$ for all $ u \in U$. If ,', is an additive mapping of $ R$ into itself satisfying $ ({u^2})' = u'u + uu'$ for all $ u \in U$, then $ (u\upsilon )' = u'\upsilon + u\upsilon '$ for all $ u,\upsilon \in U$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0722405-2
PII: S 0002-9939(1984)0722405-2
Keywords: Prime rings, Lie ideal and Jordan derivations
Article copyright: © Copyright 1984 American Mathematical Society