Abstract
Let \(R\) be a prime ring, \(L\) a noncentral Lie ideal of \(R\), \(F\) a generalized derivation with associated nonzero derivation \(d\) of \(R\). If \(a\in R\) such that \(a(d(u)^{l_1} F(u)^{l_2} d(u)^{l_3} F(u)^{l_4} \ldots F(u)^{l_k})^{n}=0\) for all \(u\in L\), where \(l_1,l_2,\ldots ,l_k\) are fixed non negative integers not all are zero and \(n\) is a fixed integer, then either \(a=0\) or \(R\) satisfies \(s_4\), the standard identity in four variables.
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Shujat, F., Khan, S. Left annihilator of generalized derivations on Lie ideals in prime rings. Rend. Circ. Mat. Palermo 64, 77–81 (2015). https://doi.org/10.1007/s12215-014-0182-6
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DOI: https://doi.org/10.1007/s12215-014-0182-6