Nonlinear skew Lie derivations on prime $$*$$ ∗ -rings

Liang Kong () and Jianhua Zhang ()
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Liang Kong: Shaanxi Normal University
Jianhua Zhang: Shaanxi Normal University

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 2, 475-484

Abstract: Abstract Let $$\mathcal {R}$$ R be a 2-torsion free unital prime $$*$$ ∗ -ring containing a nontrivial symmetric idempotent. We prove that if a map $$\phi : \mathcal {R}\rightarrow \mathcal {R}$$ ϕ : R → R satisfies $$\phi ([A, B]_{*})=[\phi (A), B]_{*}+[A, \phi (B)]_{*}$$ ϕ ( [ A , B ] ∗ ) = [ ϕ ( A ) , B ] ∗ + [ A , ϕ ( B ) ] ∗ for all $$A, B\in \mathcal {R}$$ A , B ∈ R , then $$\phi $$ ϕ is an additive $$*$$ ∗ -derivation, where $$[A, B]_{*}=AB-BA^{*}$$ [ A , B ] ∗ = A B - B A ∗ .

Keywords: Skew Lie derivation; $$*$$ ∗ -Derivation; Prime $$*$$ ∗ -ring; 16W25; 16W10 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00269-y

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