On generalized Lie derivations

  • Driss BennisEmail author
  • Hamid Reza Ebrahimi Vishki
  • Brahim Fahid
  • Mohammad Ali Bahmani


In this paper, we investigate generalized Lie derivations. We give a complete characterization of when each generalized Lie derivation is a sum of a generalized inner derivation and a Lie derivation. This generalizes a result given by Benkovič. We also investigate when every generalized Lie derivation on some particular kind of unital algebras is a sum of a generalized derivation and a central map which vanishes on all commutators. Precisely, we consider both the unital algebras with nontrivial idempotents and the trivial extension algebras.


Generalized Lie derivation Trivial extension algebra Triangular algebra 

Mathematics Subject Classification

47B47 15A78 16W25 



The authors would like to thank the referee for careful reading of the manuscript.


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Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2019

Authors and Affiliations

  1. 1.Center CeReMAR, Faculty of SciencesMohammed V UniversityRabatMorocco
  2. 2.Department of Pure Mathematics, Centre of Excellence in Analysis on Algebraic Structures (CEAAS)Ferdowsi University of MashhadMashhadIran
  3. 3.Superior School of TechnologyIbn Tofail UniversityKenitraMorocco
  4. 4.Department of Pure MathematicsFerdowsi University of MashhadMashhadIran

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