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Jordan left *-centralizers of prime and semiprime rings with involution

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Abstract

Let R be a ring with involution ′*′. An additive mapping T : R → R is called a left *-centralizer (resp. Jordan left *-centralizer) if T(xy) = T(x)y* (resp. T(x 2) = T(x)x*) holds for all \({x,y \in R}\), and a reverse left *-centralizer if T(xy) = T(y)x* holds for all \({x,y\in R}\). In the present paper, it is shown that every Jordan left *-centralizer on a semiprime ring with involution, of characteristic different from two is a reverse left *-centralizer. This result makes it possible to solve some functional equations in prime and semiprime rings with involution. Moreover, some more related results have also been discussed.

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Authors and Affiliations

  1. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

    Shakir Ali & Nadeem Ahmad Dar

  2. Department of Mathematics and Computer Science, University of Maribor FNM, Koroska 160, 2000, Maribor, Slovenia

    Joso Vukman

Authors
  1. Shakir Ali
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  2. Nadeem Ahmad Dar
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  3. Joso Vukman
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Corresponding author

Correspondence to Shakir Ali.

Additional information

This research is partially supported by the Research Grants (UGC No. 39-37/2010(SR)) and (INT/SLOVENIA/P-18/2009).

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Ali, S., Dar, N.A. & Vukman, J. Jordan left *-centralizers of prime and semiprime rings with involution. Beitr Algebra Geom 54, 609–624 (2013). https://doi.org/10.1007/s13366-012-0117-3

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  • DOI: https://doi.org/10.1007/s13366-012-0117-3

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