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Additivity of Jordan n-tuple maps on rings

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Abstract

Let \(\mathfrak {R}\) and \(\mathfrak {R}'\) be rings. We study the additivity of surjective maps \(M:\mathfrak {R}\rightarrow \mathfrak {R}'\) and \(M^{*}:\mathfrak {R}'\rightarrow \mathfrak {R}\) preserving a type of Jordan n-tuple product on these rings. We prove that if \(\mathfrak {R}\) contains a non-trivial idempotent satisfying some conditions, then they are additive. In particular, if \(\mathfrak {R}\) is a standard operator algebra, then both M and \(M^{*}\) are additive.

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Acknowledgements

We thank the anonymous reviewer for his/her careful reading of our manuscript and his/her many comments and insightful suggestions.

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Correspondence to J. C. M. Ferreira.

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Botelho, W.T., Ferreira, J.C.M. & Marietto, M.G.B. Additivity of Jordan n-tuple maps on rings. Bol. Soc. Mat. Mex. 26, 45–56 (2020). https://doi.org/10.1007/s40590-019-00240-8

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Keywords

  • Jordan n-tuple maps
  • Additivity
  • Prime rings
  • Standard operator algebras

Mathematics Subject Classification

  • 16W99
  • 47B49
  • 47L10