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International Journal of Neutrosophic Science

ISSN
Online: 2690-6805 Print: 2692-6148
Frequency

Continuous publication

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Open access · Articles freely available online · APC applies after acceptance

International Journal of Neutrosophic Science
Full Length Article

Volume 26Issue 4PP: 21-27 • 2025

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

Ali Ibrahim Mansour 1* ,
Amal A. Ibrahim 1 ,
Auday Hekmat Mahmood 1
1Department of Mathematics, College of Education, Mustansiriyah University, Baghdad, Iraq
* Corresponding Author.
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.

[6]       I. N. Herstein, Rings with Involution, The University of Chicago Press, Chicago, 1976.

[7]       E. C. Posner, "Derivations in Prime Rings," Proc. Amer. Math. Soc., vol. 8, pp. 1093-1100, 1957.

[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.

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Mansour, Ali Ibrahim, Ibrahim, Amal A., Mahmood, Auday Hekmat. "Jordan Endo Bi-AntiDerivation of 2-Torison Free Rings and Neutrosophic Rings." International Journal of Neutrosophic Science, vol. Volume 26, no. Issue 4, 2025, pp. 21-27. DOI: https://doi.org/10.54216/IJNS.260403
Mansour, A., Ibrahim, A., Mahmood, A. (2025). Jordan Endo Bi-AntiDerivation of 2-Torison Free Rings and Neutrosophic Rings. International Journal of Neutrosophic Science, Volume 26(Issue 4), 21-27. DOI: https://doi.org/10.54216/IJNS.260403
Mansour, Ali Ibrahim, Ibrahim, Amal A., Mahmood, Auday Hekmat. "Jordan Endo Bi-AntiDerivation of 2-Torison Free Rings and Neutrosophic Rings." International Journal of Neutrosophic Science Volume 26, no. Issue 4 (2025): 21-27. DOI: https://doi.org/10.54216/IJNS.260403
Mansour, A., Ibrahim, A., Mahmood, A. (2025) 'Jordan Endo Bi-AntiDerivation of 2-Torison Free Rings and Neutrosophic Rings', International Journal of Neutrosophic Science, Volume 26(Issue 4), pp. 21-27. DOI: https://doi.org/10.54216/IJNS.260403
Mansour A, Ibrahim A, Mahmood A. Jordan Endo Bi-AntiDerivation of 2-Torison Free Rings and Neutrosophic Rings. International Journal of Neutrosophic Science. 2025;Volume 26(Issue 4):21-27. DOI: https://doi.org/10.54216/IJNS.260403
A. Mansour, A. Ibrahim, A. Mahmood, "Jordan Endo Bi-AntiDerivation of 2-Torison Free Rings and Neutrosophic Rings," International Journal of Neutrosophic Science, vol. Volume 26, no. Issue 4, pp. 21-27, 2025. DOI: https://doi.org/10.54216/IJNS.260403
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