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On Generalized Jordan Derivations and Centralizers in Torsion-Free Semiprime Rings: Structural Characterizations and Equivalences

Author

Listed:
  • Abdu Madugu

    (Department of Mathematics, Faculty of Natural and Applied sciences, Umaru Musa Yar’adua University katsina, Nigeria.)

  • Tasiu Abdullahi Yusuf

    (School of Mathematical Science, Universiti Sains Malaysia. Department of Mathematics, Faculty of Natural and Applied sciences, Umaru Musa Yar’adua University katsina, Nigeria.)

Abstract

This paper investigates the structure of generalized Jordan derivations and generalized Jordan centralizers on torsion-free semiprime rings. We establish conditions under which every nonzero generalized Jordan derivation is a derivation mapping the ring into itself. Similarly, we prove that every generalized Jordan centralizer coincides with a two-sided centralizer. The approach builds upon several supporting lemmas to demonstrate that torsion-free restrictions and semiprimeness provide sufficient conditions for such equivalences. These results extend classical findings on derivations and centralizers in associative ring theory and contribute to the structural analysis of operator mappings in algebraic systems.

Suggested Citation

  • Abdu Madugu & Tasiu Abdullahi Yusuf, 2025. "On Generalized Jordan Derivations and Centralizers in Torsion-Free Semiprime Rings: Structural Characterizations and Equivalences," International Journal of Research and Innovation in Social Science, International Journal of Research and Innovation in Social Science (IJRISS), vol. 9(9), pages 3537-3542, September.
    • Handle: RePEc:bcp:journl:v:9:y:2025:issue-9:p:3537-3542
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    References listed on IDEAS

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    1. Abdu Madugu & Tasiu Abdullahi Yusuf, 2025. "A Work on Generalized Reverse Derivation and Skew-Derivation on Prime Near-Rings," International Journal of Research and Innovation in Social Science, International Journal of Research and Innovation in Social Science (IJRISS), vol. 9(4), pages 5227-5232, April.
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