Differential identities in prime rings with involution
Author:
Charles Lanski
Journal:
Trans. Amer. Math. Soc. 291 (1985), 765787
MSC:
Primary 16A38; Secondary 16A12, 16A28, 16A48, 16A72
MathSciNet review:
800262
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Abstract: Let be a prime ring with involution. Using work of V. K. Kharchenko it is shown that any generalized identity for involving derivations of and the involution of is a consequence of the generalized identities with involution which satisfies. In obtaining this result, a generalization, to rings satisfying a GPI, of the classical theorem characterizing inner derivations of finitedimensional simple algebras is required. Consequences of the main theorem are that in characteristic zero no outer derivation of can act algebraically on the set of symmetric elements of , and if the images of the set of symmetric elements under the derivations of satisfy a polynomial relation, then must satisfy a generalized polynomial identity.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947198508002629
PII:
S 00029947(1985)08002629
Article copyright:
© Copyright 1985
American Mathematical Society
