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Identities with Generalized Derivations in Prime Rings

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Abstract

In this paper we investigate identities with two generalized derivations in prime rings. We prove, for example, the following result. Let R be a prime ring of characteristic different from two and let F 1, F 2 : R → R be generalized derivations satisfying the relation F 1(x)F 2(x) + F 2(x)F 1(x) = 0 for all \({x \in R}\) . In this case either F 1 = 0 or F 2 = 0.

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Authors and Affiliations

  1. Faculty of logistics, University of Maribor, Mariborska cesta 7, 3000, Celje, Slovenia

    Maja Fošner

  2. Faculty of Natural Sciences and Mathematics, University of Maribor, Koroš ka cesta 160, 2000, Maribor, Slovenia

    Joso Vukman

Authors
  1. Maja Fošner
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  2. Joso Vukman
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Correspondence to Maja Fošner.

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Fošner, M., Vukman, J. Identities with Generalized Derivations in Prime Rings. Mediterr. J. Math. 9, 847–863 (2012). https://doi.org/10.1007/s00009-011-0158-0

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  • DOI: https://doi.org/10.1007/s00009-011-0158-0

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