Volume 26 , Issue 2 , PP: 120-131, 2025 | Cite this article as | XML | Html | PDF | Full Length Article
Thammarat Panityakul 1 , Ronnason Chinram 2 *
Doi: https://doi.org/10.54216/IJNS.260209
In this paper, we apply neutrosophic N-structures in ternary semirings. We consider ternary neutrosophic N-subsemirings of ternary semirings. We investigate the conditions for neutrosophic N-structures to be neutrosophic ternary N-subsemirings. In addition, we show the relation between ternary subsemirins and neutrosophic ternary N-subsemirins. Finally, we showed that the homomorphic preimage of the neutrosophic ternary N-subsemirings is a neutrosophic ternary N-subsemirings and the onto homomorphic image of the neutrosophic ternary N-subsemiring is also a neutrosophic ternary N-subsemirings.
Neutrosophic N-structures , Ternary semirings , Neutrosophic ternary N-subsemirings , Homomorphism , Homomorphic image
[1] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87-96, 1986. https://doi.org/10.1016/S0165-0114(86)80034-3
[2] T. K. Dutta, S. Kar, On regular ternary semirings; Advances in Algebra, Proceedings of the ICM Satellite Conference in Algebra and Related Topics, World Scientific, pp. 343-355, 2003.
[3] Y. B. Jun, K. Lee, and S. Z. Song, N-ideals of BCK/BCI-algebras, J. Chungcheong Math. Soc., vol. 22, pp. 417-437, 2009.
[4] Y. B. Jun, F. Smarandache, and H. Bordbar, Neutrosophic N-structures applied to BCK/BCI-algebras, Information, vol. 8, Article number 128, 2017. https://doi.org/10.3390/info8040128
[5] M. Khan, S. Anis, F. Smarandache, and Y. B. Jun, Neutrosophic N-structures and their applications in semigroups, Ann. Fuzzy Math. Inform., vol. 14, pp. 583-598, 2017. https://doi.org/10.30948/ afmi.2017.14.6.583
[6] D. H. Lehmer, A ternary analogue of abelian groups, American J. Math., vol. 59, pp. 329-338, 1932. https://doi.org/10.2307/2370997
[7] W. G. Lister, Ternary rings, Trans. Amer. Math. Soc., vol. 154, pp. 37–55, 1971. https://doi.org/ 10.2307/1995425
[8] G. Muhiuddin, J. C. G. John, B. Elavarasan, K. Porselvi, D. Al-Kadi, Properties of k-hybrid ideals in ternary semiring, J. Intelligent Fuzzy Syst., vol. 42, no.6, pp. 5799–5807, 2022. https://doi.org/ 10.3233/JIFS-212311
[9] P. Murugadas, Strong prime ideals in ternary semiring, Advances in Mathematics: Scientific Journal, vol. 9, no.11, pp. 9679–9684, 2020. https://doi.org/10.37418/amsj.9.11.74
[10] T. Pandiselvi, and S. Anbalagan, g-inverses in ternary semiring, Math. Stat., vol. 12, no. 5, pp. 475–483, 2024. https://doi.org/10.13189/ms.2024.120509
[11] P. Rangsuk, P. Huana and A. Iampan, Neutrosophic N-structures over UP-algebras, Neutrosophic Sets Syst., vol. 28, pp. 87-127, 2019.
[12] F. Smarandache. A Unifying Field in Logics: Neutrosophic Logic, Neutrosophy, Neutrosophic Set, Neutrosophic Probability. American Research Press, 1999.
[13] S. Z. Song, F. Smarandache, and Y. B. Jun. Neutrosophic commutative N-ideals in BCK-algebras. Information, vol. 8, Article number 130, 2017. https://doi.org/10.3390/info8040130
[14] L. A. Zadeh, Fuzzy sets, Inform. Control, vol. 8, pp. 338-353, June 1965. https://doi.org/10. 1016/S0019-9958(65)90241-X