More on the Generalized (m,n)-Jordan Derivations and Centralizers on Certain Semiprime Rings

Abstract

In this paper, we give an affirmative answer to two conjectures on generalized (mn)-Jordan derivations and generalized (mn)-Jordan centralizers raised in Ali and Fošner (Algebra Colloq 21:411–420, 2014) and Fošner (Demonstr Math 46:254–262, 2013). Precisely, when R is a semiprime ring, we prove, under some suitable torsion restrictions, that every nonzero generalized (mn)-Jordan derivation (resp., a generalized (mn)-Jordan centralizer) is a derivation (resp., a two-sided centralizer).

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Acknowledgements

The authors would like to thank the referees for their valuable comments. The results of this paper was presented by the third author in the International Conference on Algebra and its Applications (ICAA-2017) which held in April 2017 at the Faculty of Sciences and Technology, Errachidia, Morocco.

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Correspondence to Brahim Fahid.

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Bennis, D., Dhara, B. & Fahid, B. More on the Generalized (m,n)-Jordan Derivations and Centralizers on Certain Semiprime Rings. Bull. Iran. Math. Soc. 47, 217–224 (2021). https://doi.org/10.1007/s41980-020-00377-7

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Keywords

  • Semiprime ring
  • Generalized (\(\textit{m}, \textit{n}\))-derivation
  • Generalized (\(\textit{m}, \textit{n}\))-Jordan derivation
  • (\(\textit{m}, \textit{n}\))-Jordan centralizer
  • Generalized (\(\textit{m}, \textit{n}\))-Jordan centralizer

Mathematics Subject Classification

  • 16N60
  • 16W25