Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON 𝜂-GENERALIZED DERIVATIONS IN RINGS WITH JORDAN INVOLUTION

  • Phool Miyan (Department of Mathematics College of Natural and Computational Sciences Haramaya University)
  • Received : 2023.10.18
  • Accepted : 2024.02.01
  • Published : 2024.07.31
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Abstract

Let 𝒦 be a ring. An additive map 𝖚⋄ → 𝖚 is called Jordan involution on 𝒦 if (𝖚⋄)⋄ = 𝖚 and (𝖚𝖛+𝖛𝖚)⋄ = 𝖚⋄𝖛⋄+𝖛⋄𝖚⋄ for all 𝖚, 𝖛 ∈ 𝒦. If Θ is a (non-zero) 𝜂-generalized derivation on 𝒦 associated with a derivation Ω on 𝒦, then it is shown that Θ(𝖚) = 𝛄𝖚 for all u ∈ 𝒦 such that 𝛄 ∈ Ξ and 𝛄2 = 1, whenever Θ possesses [Θ(𝖚), Θ(𝖚⋄)] = [𝖚, 𝖚⋄] for all 𝖚 ∈ 𝒦.

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References

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