Compositions of derivations in prime rings (Q2756178)

Let \(R\) be a prime ring and let \(\rho\) be a right ideal of \(R\) such that \([\rho,\rho]\rho\neq 0\). Further, let \(d\) and \(\delta\) be nonzero derivations of \(R\). The first main result characterizes the situation when \(d\delta([\rho,\rho])=0\), and the second main result states that \(d\delta([\rho,\rho])\) is nonzero but contained in the center only when \(R\) has characteristic \(2\) and its central closure is of dimension \(4\) over the extended centroid.