Vanishing power values of commutators with derivations on prime rings. (Q963511)

Summary: Let \(R\) be a prime ring of \(\text{char\,}R\neq 2\), \(d\) a non-zero derivation of \(R\) and \(\rho\) a non-zero right ideal of \(R\) such that \([[d(x),x]_n,[y,d(y)]_m]^t=0\) for all \(x,y\in\rho\), where \(n\geq 0\), \(m\geq 0\), \(t\geq 1\) are fixed integers. If \([\rho,\rho]\rho\neq 0\), then \(d(\rho)\rho=0\).