Engel conditions of generalized derivations on Lie ideals and left sided ideals in prime rings and Banach Algebras

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• 作者：Basudeb Dhara ; Asma Ali ; Deepankar Das
• 关键词：Prime ring ; Derivation ; Generalized derivation ; Extended centroid ; Utumi quotient ring ; Lie ideal ; Banach algebra
• 刊名：Afrika Matematika
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：27
• 期：7-8
• 页码：1391-1401
• 全文大小：415 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics Education
  Applications of Mathematics
  History of Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：2190-7668
• 卷排序：27

文摘

Let R be a prime ring with its Utumi ring of quotients U, F a nonzero generalized derivation of R and L a noncentral Lie ideal of R. Suppose that \([F(u^{n_1}),u^{n_2},u^{n_3},\ldots ,u^{n_k}]=0\) for all \(u \in L\), where \(n_1, n_2, \ldots ,n_k\ge 1\) are fixed integers. Then one of the following holds:(1)there exists \(\alpha \in C\) such that \(F(x)=\alpha x\) for all \(x\in R\);