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 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 finite-dimensional 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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DOI:
https://doi.org/10.1090/S0002-9947-1985-0800262-9

Article copyright:
© Copyright 1985
American Mathematical Society