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On the derivations, generalized derivations and ternary derivations of degree n

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Abstract

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 the 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.

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Acknowledgements

The authors thank the referee for carefully reading the article and suggesting valuable comments that have improved the quality of this work.

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Authors and Affiliations

  1. Kashmar Higher Education Institute, Kashmar, Iran

    Amin Hosseini

  2. Department of Computer Engineering, University of Torbat Heydarieh, Torbat Heydarieh, Iran

    Mehdi Mohammadzadeh Karizaki

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  1. Amin Hosseini
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  2. Mehdi Mohammadzadeh Karizaki
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Correspondence to Mehdi Mohammadzadeh Karizaki.

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Hosseini, A., Mohammadzadeh Karizaki, M. On the derivations, generalized derivations and ternary derivations of degree n. Rend. Circ. Mat. Palermo, II. Ser 72, 2249–2264 (2023). https://doi.org/10.1007/s12215-022-00791-2

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  • DOI: https://doi.org/10.1007/s12215-022-00791-2

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