Left annihilator of generalized derivations on Lie ideals in prime rings

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• 作者：Faiza Shujat (1)
  Shahoor Khan (2)
  
  1. Department of Mathematics ; Taibah University ; Madinah ; Kingdom of Saudi Arabia
  2. Department of Mathematics ; Aligarh Muslim University ; Aligarh ; 202002 ; India
  
• 关键词：Prime ring ; Generalized derivation ; Extended centroid ; Utumi quotient ring ; 16N60 ; 16U80 ; 16W25
• 刊名：Rendiconti del Circolo Matematico di Palermo
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：64
• 期：1
• 页码：77-81
• 全文大小：119 KB
• 参考文献：1. Beidar, KI, Martindale, WS, Mikhalev, AV (1996) Rings with Generalized Identities, Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker, Inc., New York
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  21. Lee, TK (1992) Semiprime rings with differential identities. Bull. Inst. Math. Acad. Sinica 20: pp. 27-38
  22. Lee, TK (1999) Generalized derivations of left faithful rings. Comm. Algebra 27: pp. 4057-4073 CrossRef
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebra
  Geometry
  Analysis
  Applications of Mathematics
  
• 出版者：Springer Milan
• ISSN：1973-4409

文摘

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.