English

Abstract

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.