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JORDAN HIGHER DERIVATIONS ON TRIVIAL EXTENSION ALGEBRAS
Vishki, Hamid Reza Ebrahimi,Mirzavaziri, Madjid,Moafian, Fahimeh Korean Mathematical Society 2016 대한수학회논문집 Vol.31 No.2
We first give the constructions of (Jordan) higher derivations on a trivial extension algebra and then we provide some sufficient conditions under which a Jordan higher derivation on a trivial extension algebra is a higher derivation. We then proceed to the trivial generalized matrix algebras as a special trivial extension algebra. As an application we characterize the construction of Jordan higher derivations on a triangular algebra. We also provide some illuminating examples of Jordan higher derivations on certain trivial extension algebras which are not higher derivations.
JORDAN GENERALIZED DERIVATIONS ON TRIVIAL EXTENSION ALGEBRAS
Bahmani, Mohammad Ali,Bennis, Driss,Vishki, Hamid Reza Ebrahimi,Attar, Azam Erfanian,Fahid, Barahim Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.3
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]).