Left annihilator of generalized derivations on Lie ideals in prime rings |
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Authors: | Email author" target="_blank">Faiza?ShujatEmail author Shahoor?Khan |
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Institution: | 1.Department of Mathematics,Taibah University,Madinah,Kingdom of Saudi Arabia;2.Department of Mathematics,Aligarh Muslim University,Aligarh,India |
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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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