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Polynomial preserving maps on certain Jordan algebras

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Abstract

LetB andQ be associative algebras and letS be a Jordan subalgebra ofB. Letf(x 1,…,x m ) be a (noncommutative) multilinear polynomial such thatS is closed underf. Letα:S→Q be anf-homomorphism in the sense that it is a linear map preservingf. Under suitable conditions it is shown thatα is essentially given by a ring homomorphism. An analogous theorem forf-derivations is also proved. The proofs rest heavily on results concerning functional identities andd-freeness.

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Authors and Affiliations

  1. Department of Mathematics, National Cheng-Kung University, Tainan, Taiwan

    K. I. Beidar

  2. Department of Mathematics, University of Maribor, Maribor, Slovenia

    M. Brešar

  3. Department of Mechanics and Mathematics, Tula State University, Tula, Russia

    M. A. Chebotar

  4. Department of Mathematics, University of Massachusetts, Amherst, USA

    W. S. Martindale

Authors
  1. K. I. Beidar
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  2. M. Brešar
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  3. M. A. Chebotar
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  4. W. S. Martindale
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Corresponding author

Correspondence to K. I. Beidar.

Additional information

The second author was partially supported by a grant from the Ministry of Science of Slovenia.

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Beidar, K.I., Brešar, M., Chebotar, M.A. et al. Polynomial preserving maps on certain Jordan algebras. Isr. J. Math. 141, 285–313 (2004). https://doi.org/10.1007/BF02772225

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  • DOI: https://doi.org/10.1007/BF02772225

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