Volume 25 • Issue 4 • PP: 169-175 • 2025
Neutrosophic Ideal of a Near Algebra
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
This article introduces the idea of neutrosophic ideal of a near algebra and provides a definition and example. A few fundamental features related to this approach are also explored. We also present the topics neutrosophic near algebra homomorphism, kernel of a neutrosophic near algebra and coset of a neutrosophic ideal of a near algebra. It is been briefed with the appropriate definitions and theorems on it. It is been proved that sum of the right neutrosophic ideal of a near algebra is also a right neutrosophic ideal of a near algebra over a neutrosophic field.
Keywords
References
[1] A. A. Agboola and B. Davvaz, "Introduction to neutrosophic nearrings," Annals of Fuzzy Mathematics and Informatics, vol. 12, no. 3, pp. 397–410, 2016.
[2] A. A. Agboola and S. A. Akinleye, "Neutrosophic vector spaces," Neutrosophic Sets and Systems, vol. 4, 2014.
[3] A. A. Agboola, A. D. Akinola, and O. Y. Oyebola, "Neutrosophic Rings I," International Journal of Mathematical Combinatorics, vol. 4, pp. 1–14, 2011.
[4] A. A. Agboola, A. O. Akwu, and Y. T. Oyebo, "Neutrosophic groups and Neutrosophic Subgroups," International Journal of Mathematical Combinatorics, vol. 3, pp. 1–9, 2012.
[5] L. Bhaskar, P. Narasimha Swamy, and G. Nanaji Rao, "Vague Γ- Near Algebra over Vague Field," Southeast Asian Bulletin of Mathematics, vol. 48, pp. 15–22, 2024.
[6] H. Brown, "Near algebra," Illinois Journal of Mathematics, vol. 12, pp. 215–227, 1968.
[7] Harika, K. Rajani, P. Narasimha Swamy, T. Nagaiah, and L. Bhaskar, "Neutrosophic near algebra over neutrosophic field," International Journal of Neutrosophic Science, vol. 22, no. 2, pp. 29–34, 2023.
[8] H. Bhurgula, N. S. Pasham, R. Bandaru, and A. S. Alali, "Hybrid near algebra," Axioms, vol. 12, p. 877, 2023.
[9] P. Narasimha Swamy, B. Harika, K. Vijay Kumar, B. Jyothi, and K. Rajani, "A note on Hybrid Coset of a Nearring," Communications on Applied Nonlinear Analysis, vol. 31, no. 2, 2024.
[10] T. Nagaiah, L. Bhaskar, P. Narasimha Swamy, and S. Broumi, "A Study on Neutrosophic Algebra," Neutrosophic Sets and Systems, vol. 50, 2022.
[11] G. Pilz, Near-ring. Amsterdam: North-Holland Publishers, 1983.
[12] F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic, Neutrosophy, Neutrosophic Set, Neutrosophic Probability. Rehoboth: American Research Press, 2003.
[13] W. B. Vasantha Kanda Swamy and F. Smarandache, Fuzzy Algebra. Rehoboth: American Research Press, 2003.
[14] W. B. Vasantha Kanda Swamy and F. Smarandache, Basic Neutrosophic Algebraic Structures and Their Applications to Fuzzy and Neutrosophic Models. Church Rock: Hexis, 2004.
[15] L. A. Zadeh, "Fuzzy sets," Information and Control, vol. 8, pp. 338–353, 1965.
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.