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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Differential identities in prime rings with involution
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by Charles Lanski PDF
Trans. Amer. Math. Soc. 291 (1985), 765-787 Request permission

Correction: Trans. Amer. Math. Soc. 309 (1988), 857-859.

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
  • © Copyright 1985 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 291 (1985), 765-787
  • MSC: Primary 16A38; Secondary 16A12, 16A28, 16A48, 16A72
  • DOI: https://doi.org/10.1090/S0002-9947-1985-0800262-9
  • MathSciNet review: 800262