Let R be a noncommutative prime ring of characteristic different from 2, with its two-sided Martindale quotient ring Q, C the extended centroid of R and a ∈ R. Suppose that δ is a nonzero σ-derivation of R such that a[δ(xn), xn]k = 0 for all x ∈ R, where σ is an automorphism of R, n and k are fixed positive integers. Then a = 0.
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Pehlivan, T., Albas, E. Annihilators of Skew Derivations with Engel Conditions on Prime Rings. Czech Math J 70, 587–603 (2020). https://doi.org/10.21136/CMJ.2019.0412-18
- prime ring
- skew derivation