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On the derivations‎, ‎generalized derivations and ternary derivations of degree $n$
  • Amin Hosseini,
  • Mehdi Mohammadzadeh Karizaki
Amin Hosseini
Kashmar Higher Education Institute, Kashmar, Iran

Corresponding Author:[email protected]

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Mehdi Mohammadzadeh Karizaki
Departemant of computer engineering
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‎In this paper‎, ‎we introduce the concepts of derivation of degree $n$‎, ‎generalized derivation of degree $n$ and ternary derivation of degree $n$‎, ‎where $n$ is a positive integer‎, ‎and then we study algebraic properties of these mappings‎. ‎For instance‎, ‎we study the image of derivations of degree $n$ on algebras and in this regard we prove that‎, ‎under certain conditions‎, ‎every derivation of degree $n$ on an algebra maps the algebra into its Jacobson radical‎. ‎Also‎, ‎we present some characterizations of these mappings on algebras‎. ‎For example‎, ‎under certain assumptions‎, ‎we show that if $f$ is an additive generalized derivation of degree $n$ with an associated mapping $d$‎, ‎then either $f$ is a linear generalized derivation with the associated linear derivation $d$ or $f$ and $d$ are identically zero‎. ‎Some other related results are also established‎.
03 Aug 2022Published in Rendiconti del Circolo Matematico di Palermo Series 2. 10.1007/s12215-022-00791-2