Volume 26 • Issue 2 • PP: 292-298 • 2025
Study Neutrosophic Quasi-Frobenius by Local and Artinian Rings
Open Access & Copyright
© 2025 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
View PDF 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
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
Choose your preferred format
Publisher's Note
The statements, opinions, and data presented in this article are solely those of the author(s) and do not necessarily represent those of ASPG, the journal, or its editors. ASPG and the editors disclaim responsibility for any harm arising from the use of any ideas, methods, instructions, or products described in this article, to the fullest extent permitted by applicable law.