Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2018; 33(3): 721-739

Online first article July 9, 2018      Printed July 31, 2018

https://doi.org/10.4134/CKMS.c170284

Copyright © The Korean Mathematical Society.

Jordan generalized derivations on trivial extension algebras

Mohammad Ali Bahmani, Driss Bennis, Hamid Reza Ebrahimi Vishki, Azam Erfanian Attar, Barahim Fahid

Ferdowsi University of Mashhad, Faculty of Sciences, Ferdowsi University of Mashhad, Ferdowsi University of Mashhad, Faculty of Sciences

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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]).

Keywords: trivial extension algebra, triangular algebra, Jordan derivation, Jordan generalized derivation, $f$-generalized derivation

MSC numbers: 15A78, 16W25, 47B47

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