• Bahmani, Mohammad Ali (Department of Pure Mathematics Ferdowsi University of Mashhad) ;
  • Bennis, Driss (Department of Mathematics Faculty of Sciences) ;
  • Vishki, Hamid Reza Ebrahimi (Department of Pure Mathematics Centre of Excellence in Analysis on Algebraic Structures (CEAAS) Ferdowsi University of Mashhad) ;
  • Attar, Azam Erfanian (Department of Pure Mathematics Ferdowsi University of Mashhad) ;
  • Fahid, Barahim (Department of Mathematics Faculty of Sciences B.P. 1014, Mohammed V University in Rabat)
  • Received : 2017.07.11
  • Accepted : 2017.11.02
  • Published : 2018.07.31


In this paper, we investigate the problem of describing the form of Jordan generalized derivations on trivial extension algebras. One of the main results shows, under some conditions, that every Jordan generalized derivation on a trivial extension algebra is the sum of a generalized derivation and an antiderivation. This result extends the study of Jordan generalized derivations on triangular algebras (see [12]), and also it can be considered as a "generalized" counterpart of the results given on Jordan derivations of a trivial extension algebra (see [11]).


trivial extension algebra;triangular algebra;Jordan derivation;Jordan generalized derivation;f-generalized derivation


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