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Annihilators of skew derivations with Engel conditions on prime rings

Taylan Pehlivan;  Emine Albas — 2020

Czechoslovak Mathematical Journal

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 ( x n ) , x n ] 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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