A generalization of Engel conditions with derivations in rings

摘要

Let R be a prime ring of characteristic different from 2 with Z the center of R and d a nonzero derivation of R. Let k, m, n be fixed positive integers. If (d(x~k), x~k_n)m ∈ Z for all x ∈ R, then R satisfies S_4, the standard identity in 4 variables.