Afrika Matematika, Volume (31), Year (2020-6) , Pages (423-435)

Title : ( On generalized Lie derivations )

Authors: Driss Bennis , Hamid Reza Ebrahimi Vishki , Brahim Fahid , mohammad ali bahmani ,

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Abstract

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 Benkovic. 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.

Keywords

, Generalized Lie derivation, Trivial extension algebra, Triangular algebra