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On symmetric Jordan and Jordan left bi-derivations of prime rings

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Abstract

In this paper, we investigated some properties of symmetric Jordan bi-derivation and symmetric Jordan left bi-derivation for associative rings. We showed that for an associative prime ring with \(charR\ne 2\) if D is a symmetric Jordan bi-derivation then D is symmetric bi-derivation. And also we showed that for a 2-torsion free and 3-torsion free prime ring, if there exists a nonzero symmetric Jordan left bi-derivation D then R is commutative.

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  1. Department of Mathematics, Faculty of Arts and Sciences, Süleyman Demirel University, 32260, Isparta, Turkey

    Yılmaz Çeven & Zekiye Çiloğlu

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  1. Yılmaz Çeven
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  2. Zekiye Çiloğlu
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Correspondence to Yılmaz Çeven.

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Çeven, Y., Çiloğlu, Z. On symmetric Jordan and Jordan left bi-derivations of prime rings. Afr. Mat. 29, 689–698 (2018). https://doi.org/10.1007/s13370-018-0570-8

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  • DOI: https://doi.org/10.1007/s13370-018-0570-8

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