Annihilating and Engel conditions on right ideals with generalized derivations

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• 作者：Vincenzo De Filippis ; Giovanni Scudo
• 关键词：Generalized derivation ; Prime ring ; Differential identity ; 16W25 ; 16N60
• 刊名：Beitr?ge zur Algebra und Geometrie / Contributions to Algebra and Geometry
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：57
• 期：1
• 页码：155-172
• 全文大小：487 KB
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  Shiue, W.K.: Annihilators of derivations with Engel conditions on one-sided ideals. Publ. Math. Debrecen 62, 237–243 (2003a)MathSciNet MATH
  Shiue, W.K.: Annihilators of derivations with Engel conditions on Lie ideals. Rend. Circ. Mat. Palermo Serie II Tomo LII, pp. 505–509 (2003b)
  
• 作者单位：Vincenzo De Filippis (1)
  Giovanni Scudo (1)
  
  1. Department of Mathematics and Computer Science, University of Messina, Messina, Italy
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algebra
  Convex and Discrete Geometry
  Geometry
  Algebraic Geometry
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：2191-0383

文摘

Let \(R\) be a prime ring of characteristic different from \(2\), \(U\) its right Utumi quotient ring, \(C\) its extended centroid, \(G\) a non-zero generalized derivation of \(R\), \(a\ne 0\) be an element of \(R\), \(I\) a non-zero right ideal of \(R\) such that \(s_4(I,\ldots ,I)I\ne 0\) and \(n,k\ge 1\) fixed integers. If \(a[G([r_1,r_2]^n),[r_1,r_2]^n]_k=0\), for any \(r_1,r_2 \in I\), then either there exist \(c \in U\) and \(\gamma \in C\), such that \(G(x)=cx\) and \((c-\gamma )I=0\), or \(aI=aG(I)=0\). Keywords Generalized derivation Prime ring Differential identity