On centrally-extended maps on rings

详细信息    查看全文

• 作者：H. E. Bell ; M. N. Daif
• 关键词：Derivations ; Epimorphisms ; Centrally ; extended derivations ; Centrally ; extended epimorphisms ; Commutativity theorems ; 16W25 ; 16U80 ; 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：129-136
• 全文大小：358 KB
• 参考文献：Ali, S., Huang, S.: On derivations in semiprime rings. Algebras Represent. Theory 15(6), 1023–1033 (2012)CrossRef MathSciNet MATH
  Bell, H.E., Daif, M.N.: On commutativity and strong commutativity-preserving maps. Can. Math. Bull. 37(4), 443–447 (1994)CrossRef MathSciNet MATH
  Bell, H.E., Martindale, W.S.: Centralizing mappings of semiprime rings. Can. Math. Bull. 30(1), 92–101 (1987)CrossRef MathSciNet MATH
  Liu, C.-K.: On skew derivations in semiprime rings. Algebras Represent. Theory 16(6), 1561–1576 (2013)CrossRef MATH
  
• 作者单位：H. E. Bell (1)
  M. N. Daif (2)
  
  1. Department of Mathematics, Brock University, St. Catharines, ON, L2S 3A1, Canada
  2. Department of Mathematics, Al-Azhar University, Nasr City, Cairo, 11884, Egypt
  
• 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 ring with center \(Z\). A map \(D\) of \(R\) (resp. \(T\) of \(R\)) is called a centrally-extended derivation (resp. a centrally-extended endomorphism) if for each \(x,y\in R, D(x+y)-D(x)-D(y)\in Z\) and \(D(xy)-D(x)y-xD(y)\in Z\) (resp. \(T(x+y)-T(x)-T(y)\in Z\) and \(T(xy)-T(x)T(y)\in Z\)). We discuss existence of such maps which are not derivations or endomorphisms, we study their effect on \(Z\), and we give some commutativity results. Keywords Derivations Epimorphisms Centrally-extended derivations Centrally-extended epimorphisms Commutativity theorems