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<p>Let <i>R</i> be a 2-torsion free prime ring and let <i>θ, φ</i> be endomorphisms of <i>R</i>. We prove that if <i>R</i> is commutative, then every Jordan triple (<i>θ, φ</i>)-derivation of <i>R</i> is a (<i>θ, φ</i>)-derivation and if <i>R</i> is noncommutative, then every Jordan triple (<i>θ, φ</i>)-derivation of <i>R</i> with either <i>θ</i> or <i>φ</i> an epimorphism, is a (<i>θ, φ</i>)-derivation. As an application, we characterize Jordan triple semiderivations of prime rings. Our theorems naturally generalize the result for Jordan (<i>θ, φ</i>)-derivations obtained by M. Brešar, J. Vukman (1991) and the result for Jordan semiderivations obtained by V. De Filippis, A. Mamouni, L. Oukhtite (2015).</p>

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Jordan triple (θ, φ)-derivations of prime rings

  • 期刊论文

  • 发表日期：

    2025年9月4日

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  • Tzu-Ying Kao,
  • Cheng-Kai Liu

摘要

Let R be a 2-torsion free prime ring and let θ, φ be endomorphisms of R. We prove that if R is commutative, then every Jordan triple (θ, φ)-derivation of R is a (θ, φ)-derivation and if R is noncommutative, then every Jordan triple (θ, φ)-derivation of R with either θ or φ an epimorphism, is a (θ, φ)-derivation. As an application, we characterize Jordan triple semiderivations of prime rings. Our theorems naturally generalize the result for Jordan (θ, φ)-derivations obtained by M. Brešar, J. Vukman (1991) and the result for Jordan semiderivations obtained by V. De Filippis, A. Mamouni, L. Oukhtite (2015).