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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 26 , Issue 4 , PP: 21-27, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

Jordan Endo Bi-AntiDerivation of 2-Torison Free Rings and Neutrosophic Rings

Ali Ibrahim Mansour 1 * , Amal A. Ibrahim 2 , Auday Hekmat Mahmood 3

  • 1 Department of Mathematics, College of Education, Mustansiriyah University, Baghdad, Iraq - (aliibrahimaltaay@uomustansiriyah.edu.iq)
  • 2 Department of Mathematics, College of Education, Mustansiriyah University, Baghdad, Iraq - (amal.ibrahim@uomustansiriyah.edu.iq)
  • 3 Department of Mathematics, College of Education, Mustansiriyah University, Baghdad, Iraq - (audaymath@uomustansiriyah.edu.iq)

    • Doi: https://doi.org/10.54216/IJNS.260403

    Received: February 25, 2025 Revised: April 22, 2025 Accepted: June 10, 2025
    Abstract

    Let  be the direct product of an associative ring . In the work the concepts of Endo Bi-Antiderivation, Jordan Endo Bi-Antiderivation and Quasi Endo Bi-Antiderivation on a ring  are introduced, furthermore the relations between these bi-additive mappings are given. As essential point, we searched for appropriate conditions that make equivalence between Jordan Endo Bi-Antiderivation and Quasi Endo Bi-Antiderivation. Also, we prove the same results for the generalized case of neutrosophic rings.

    Keywords :

    Direct product of ring , Prime rings , Bi-additive mapping , Neutrosophic ring

    References

    [1]       H. M. Auday, S. N. Mahdi, and M. S. Salah, "Generalized Higher Derivation on ΓM-Modules," Iraqi J. Sci., special Issue, pp. 35-44, 2020.

    [2]       M. N. Rahman and A. C. Paul, "Jordan derivations on 2-torsion free semiprime Γ-Rings," J. Bangladesh Acad. Sci., vol. 38, no. 2, pp. 189-195, 2014.

    [3]       N. Argac, "On Prime and Semiprime Rings with Derivations," Algebra Colloquium, vol. 13, no. 3, pp. 237-246, 2006.

    [4]       H. M. Auday, J. A. Alan, and S. N. Mahdi, "Relatively Commuting Mapping and Symmetric Biderivation in Semirings," JEAS, vol. 13, no. 1, pp. 10932-10935, 2018.

    [5]       M. Bresar, "Commuting traces of biadditive mappings, commutativity preserving mappings and Lie mappings," Trans. Amer. Math. Soc., vol. 335, pp. 525-546, 1993.

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    [8]       G. Maksa, "Remark on symmetric biadditive functions having non-negative diagonalization," Glasnik Math., vol. 15, pp. 279-280, 1980.

    [9]       J. Vokman, "Symmetric Bi-derivations on Prime and Semiprime Rings," Aequationes Math., vol. 38, pp. 181-189, 1989.

    [10]    M. Bresar, "On generalized Biderivations and Related map," University of Maribor, PF, Koroska 160, 62000 Maribor, Slovenia, 1994, pp. 764-786.

    [11]    M. Bresar and J. Vokman, "Orthogonal derivations and an extension of Theorem of Posner," Radovi Matematicki, vol. 5, pp. 237-246, 1991.

    [12]    M. Abobala, "On the Characterization of Maximal and Minimal Ideals In Several Neutrosophic Rings," Neutrosophic Sets Syst., 2021.

    [13]    M. Abobala, "A Study Of Maximal and Minimal Ideals Of n-Refined Neutrosophic Rings," J. Fuzzy Extens. Appl., 2021.

    [14]    V. W. B. Kandasamy and F. Smarandache, "Some Neutrosophic Algebraic Structures and Neutrosophic N-Algebraic Structures," Hexis, Phoenix, Arizona, 2006.

    Cite This Article As :
    Ibrahim, Ali. , A., Amal. , Hekmat, Auday. Jordan Endo Bi-AntiDerivation of 2-Torison Free Rings and Neutrosophic Rings. International Journal of Neutrosophic Science, vol. , no. , 2025, pp. 21-27. DOI: https://doi.org/10.54216/IJNS.260403
    Ibrahim, A. A., A. Hekmat, A. (2025). Jordan Endo Bi-AntiDerivation of 2-Torison Free Rings and Neutrosophic Rings. International Journal of Neutrosophic Science, (), 21-27. DOI: https://doi.org/10.54216/IJNS.260403
    Ibrahim, Ali. A., Amal. Hekmat, Auday. Jordan Endo Bi-AntiDerivation of 2-Torison Free Rings and Neutrosophic Rings. International Journal of Neutrosophic Science , no. (2025): 21-27. DOI: https://doi.org/10.54216/IJNS.260403
    Ibrahim, A. , A., A. , Hekmat, A. (2025) . Jordan Endo Bi-AntiDerivation of 2-Torison Free Rings and Neutrosophic Rings. International Journal of Neutrosophic Science , () , 21-27 . DOI: https://doi.org/10.54216/IJNS.260403
    Ibrahim A. , A. A. , Hekmat A. [2025]. Jordan Endo Bi-AntiDerivation of 2-Torison Free Rings and Neutrosophic Rings. International Journal of Neutrosophic Science. (): 21-27. DOI: https://doi.org/10.54216/IJNS.260403
    Ibrahim, A. A., A. Hekmat, A. "Jordan Endo Bi-AntiDerivation of 2-Torison Free Rings and Neutrosophic Rings," International Journal of Neutrosophic Science, vol. , no. , pp. 21-27, 2025. DOI: https://doi.org/10.54216/IJNS.260403

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