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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Differential identities in prime rings with involution


Author: Charles Lanski
Journal: Trans. Amer. Math. Soc. 291 (1985), 765-787
MSC: Primary 16A38; Secondary 16A12, 16A28, 16A48, 16A72
MathSciNet review: 800262
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Abstract: Let $ R$ be a prime ring with involution. Using work of V. K. Kharchenko it is shown that any generalized identity for $ R$ involving derivations of $ R$ and the involution of $ R$ is a consequence of the generalized identities with involution which $ R$ satisfies. In obtaining this result, a generalization, to rings satisfying a GPI, of the classical theorem characterizing inner derivations of finite-dimensional simple algebras is required. Consequences of the main theorem are that in characteristic zero no outer derivation of $ R$ can act algebraically on the set of symmetric elements of $ R$, and if the images of the set of symmetric elements under the derivations of $ R$ satisfy a polynomial relation, then $ R$ must satisfy a generalized polynomial identity.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0800262-9
PII: S 0002-9947(1985)0800262-9
Article copyright: © Copyright 1985 American Mathematical Society