International Journal of Neutrosophic Science

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Volume 26 , Issue 2 , PP: 292-298, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

Study Neutrosophic Quasi-Frobenius by Local and Artinian Rings

Omar A. Khashan 1 * , Majid M. Abed 2

  • 1 Department of Mathematics, College of Computer Sciences and Mathematics, University of Tikrit, Tikrit, Iraq - (omar1990@st.tu.edu.iq)
  • 2 Department of Mathematics, College of Education for Pure Science, University Of Anbar, Ramadi, Anbar, Iraq - (majid_math@uoanbar.edu.iq)
  • Doi: https://doi.org/10.54216/IJNS.260222

    Received: December 27, 2024 Revised: February 07, 2025 Accepted: March 14, 2025
    Abstract

    In this paper, we study the relationships between the Neutrosophic quasi-Frobenius rings and the Neutrosophic of local rings and Artinian rings. In addition, we present study the relationship between the Neutrosophic quasi-Frobenius ring and some concepts such as Neutrosophic semisimple ring, Neutrosophic module injective and Neutrosophic Noetherian ring. Finally, we introduce some mathematical formulas with an commutative, coherent and Neutrosophic perfect ring, through which we obtain the Neutrosophic quasi-Frobenius ring.

    Keywords :

    Quasi-Frobenius rings , Artinian rings , Local rings , Noetherian ring

    References

    [1]      T. Nakayama, "On Frobeniusian algebras. II," Ann. Math., vol. 42, pp. 1–21, 1941.

    [2]      M. Ikeda and T. Nakayama, "Supplementary remarks on Frobeniusian algebras. II," Osaka Math. J., vol. 2, pp. 7–12, 1950.

    [3]      K. Morita and H. Tachikawa, "Character modules, submodules of a free module, and quasi-Frobenius rings," Math. Z., vol. 65, pp. 414–428, 1956.

    [4]      J. Dieudonné, "Remarks on quasi-Frobenius rings," Illinois J. Math., vol. 2, pp. 346–354, 1958.

    [5]      C. Faith and E. A. Walker, "Characterizations of quasi-Frobenius rings," Notices Amer. Math. Soc., vol. 11, p. 766, 1964.

    [6]      D. Van Huynh, "Note on quasi-Frobenius rings," Proc. Amer. Math. Soc., vol. 124, no. 2, pp. 459–464, 1996.

    [7]      M. S. Elaraby and M. Abdul-Mageed, "Deep models for Arabic named entity recognition: Exploring representations and transfer learning," Comput. Speech Lang., vol. 65, p. 101113, 2021.

    [8]      L. A. Zadeh, "Fuzzy sets," Inf. Control, vol. 8, no. 3, pp. 338–353, 1965.

    [9]      K. T. Atanassov, "Intuitionistic fuzzy sets," Fuzzy Sets Syst., vol. 20, pp. 87–96, 1986.

    [10]   A. M. Al-Khatib and M. A. Al-Taani, "Arabic named entity recognition using deep learning approaches," J. King Saud Univ. - Comput. Inf. Sci., vol. 34, no. 6, pp. 2796–2803, 2022.

    [11]   F. Smarandache, Ed., Proceedings of the First International Conference on Neutrosophy, Neutrosophic Set, Neutrosophic Probability and Statistics, Univ. New Mexico, 2001.

    [12]   L. W. Small, Ed., Noetherian Rings and Their Applications, vol. 24, Amer. Math. Soc., 1987.

    [13]   G. S. Monk, "A characterization of exchange rings," Proc. Amer. Math. Soc., vol. 35, no. 2, pp. 349–353, 1972.

    [14]   L. H. Rowen, Ring Theory, Academic Press, 1991.

    [15]   S. Glaz, Commutative Coherent Rings, vol. 1371, Springer, 2006.

    [16]   F. Kasch, Modules and Rings, vol. 17, Academic Press, 1982.

    [17]   F. Siddiqua, Study on Semisimple Rings and Modules, 2021.

    [18]   P. A. Guil Asensio, S. Sahinkaya, and A. K. Srivastava, "New characterizations of pseudo-Frobenius rings and a generalization of the FGF conjecture," Israel J. Math., vol. 214, no. 1, pp. 121–148, 2016.

    [19]   T. Y. Lam, A First Course in Noncommutative Rings, Springer, 1991.

    [20]   T. Y. Lam, Lectures on Modules and Rings, vol. 189, Springer, 2012.

    [21]   C. Hajarnavis, Ring Theory (MA4H8), 2011.

    [22]   D. Van Huynh and N. V. Dung, "A characterization of Artinian rings," Glasgow Math. J., vol. 30, no. 1, pp. 67–73, 1988.

    [23]   E. H. Feller, "Noetherian modules and Noetherian injective rings," Tohoku Math. J., vol. 20, no. 1, pp. 119–133, 1968.

    [24]   E. Matlis, "Injective modules over Noetherian rings," Pac. J. Math., vol. 8, pp. 511–528, 1959.

    Cite This Article As :
    A., Omar. , M., Majid. Study Neutrosophic Quasi-Frobenius by Local and Artinian Rings. International Journal of Neutrosophic Science, vol. , no. , 2025, pp. 292-298. DOI: https://doi.org/10.54216/IJNS.260222
    A., O. M., M. (2025). Study Neutrosophic Quasi-Frobenius by Local and Artinian Rings. International Journal of Neutrosophic Science, (), 292-298. DOI: https://doi.org/10.54216/IJNS.260222
    A., Omar. M., Majid. Study Neutrosophic Quasi-Frobenius by Local and Artinian Rings. International Journal of Neutrosophic Science , no. (2025): 292-298. DOI: https://doi.org/10.54216/IJNS.260222
    A., O. , M., M. (2025) . Study Neutrosophic Quasi-Frobenius by Local and Artinian Rings. International Journal of Neutrosophic Science , () , 292-298 . DOI: https://doi.org/10.54216/IJNS.260222
    A. O. , M. M. [2025]. Study Neutrosophic Quasi-Frobenius by Local and Artinian Rings. International Journal of Neutrosophic Science. (): 292-298. DOI: https://doi.org/10.54216/IJNS.260222
    A., O. M., M. "Study Neutrosophic Quasi-Frobenius by Local and Artinian Rings," International Journal of Neutrosophic Science, vol. , no. , pp. 292-298, 2025. DOI: https://doi.org/10.54216/IJNS.260222