Lie ideals and annihilator conditions on power values of commutators with derivation (Q5939118)

Let \(R\) be a prime ring, \(\text{char }R\neq 2\), \(Z(R)\) the center of \(R\), \(D\neq 0\) a derivation of \(R\), \(L\) a noncentral Lie ideal of \(R\), and \(n\geq 1\) a fixed integer. The main result in the paper is: if \(a\in R\) with \(a[D(y),y]^n\in Z(R)\) for all \(y\in L\) then \(a=0\) or \(R\) satisfies the standard identity \(S_4\). To prove this the author shows first that when all \(a[D(y),y]^n=0\) then \(a=0\). The statements of Theorem 1 and of Theorem 2 on the first page of the paper should be interchanged.