1
Department of Mathematics, Government Arts College (affiliated to Bharathidasan University), Thanthonimalai, Karur 639005, Tamilnadu, India
(a.priya@gackarur.ac.in)
2
Department of Mathematics, Thanthai Periyar Government Arts and Science College (affiliated to Bharathidasan University), Tiruchirappalli 624024, Tamilnadu, India
(maragathameenakship@gmail.com)
3
Fuzzy Algebras and Decision-Making Problems Research Unit, School of Science, University of Phayao, 19 Moo 2, Tambon Mae Ka, Amphur Mueang, Phayao 56000, Thailand
(aiyared.ia@up.ac.th)
4
Department of Mathematics, Rajah Serfoji Government College, Thanjavur 613005, Tamilnadu, India
(nrajesh topology@yahoo.co.in)
Abstract :
The notion of neutrosophic nil radicals of neutrosophic ideals in rings is introduced, and related properties are investigated. In addition, we study some relations between the nil radical of the neutrosophic polynomial ideal of the polynomial ring R[x] induced by a neutrosophic ideal of a ring R and the nil radical of a neutrosophic ideal of R. Finally, we find the result of neutrosophic nil radicals of neutrosophic ideals from the epimorphism of rings.
Keywords :
ring; neutrosophic polynomial ideal; neutrosophic ideal; neutrosophic nil radical; epimorphism.
References :
[1] B. Ahmad and A. Kharal, On fuzzy soft sets, Advances in Fuzzy Systems, 2009, (2009), Article ID 586507, 6 pages.
[2] K. T. Atanassov, Intuitionistic sets, Fuzzy Sets and Systems, 20(1), (1986), 87-96.
[3] M. Atef, M. I. Ali, and T. M. Al-Shami, Fuzzy soft covering based multi-granulation fuzzy rough sets and their applications, Computational and Applied Mathematics, 40(4), (2021), 115.
[4] N. Caˇgman, S. Enginoˇglu, and F. Citak, Fuzzy soft set theory and its application, Iranian Journal of Fuzzy Systems, 8(3), (2011), 137-147.
[5] V. Cetkin and H. Aygun, An approach to neutrosophic ideals, Universal Journal of Mathematics and Applications, 1(2), (2018), 132-136.
[6] H. Garg and S. Singh, A novel triangular interval type-2 intuitionistic fuzzy set and their aggregation operators, Iranian Journal of Fuzzy Systems, 15(5), (2018), 69-93.
[7] H. Garg and K. Kumar, An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making, Soft Computing, 22(15), (2018), 4959-4970.
[8] H. Garg and K. Kumar, Distance measures for connection number sets based on set pair analysis and its applications to decision-making process, Applied Intelligence, 48(10), (2018), 3346-3359.
[9] M. S. Hameed, Z. Ahmad, and S. Ali, Characterization of γ-single valued neutrosophic rings and ideals, Neutrosophic Sets and Systems, 50, (2022), 47-63.
[10] A. Priya, P. Maragatha Meenakshi, A. Iampan, and N. Rajesh, Polynomial ideals of a ring based on neutrosophic sets, International Journal of Neutrosophic Science, 22(4), 2023, 8-19.
[11] F. Smarandache, A unifying field in logics: neutrosophic logic, neutrosophy, neutrosophic set, neutrosophic probability, American Research Press, Rehoboth, New Mexico, (1999).
[12] F. Smarandache, Neutrosophic set-a generalization of the intuitionistic fuzzy set, International Journal of Pure and Applied Mathematics, 24(3), (2005), 287-297.
[13] L. A. Zadeh, Fuzzy sets, Information and control, 8(3), (1965), 338-353.
| Style | # |
|---|---|
| MLA | A. Priya, P. Maragatha Meenakshi, Aiyared Iampan, N. Rajesh. "Neutrosophic nil radicals of neutrosophic ideals in rings." International Journal of Neutrosophic Science, Vol. 22, No. 4, 2023 ,PP. 82-92 (Doi : https://doi.org/10.54216/IJNS.220407) |
| APA | A. Priya, P. Maragatha Meenakshi, Aiyared Iampan, N. Rajesh. (2023). Neutrosophic nil radicals of neutrosophic ideals in rings. Journal of International Journal of Neutrosophic Science, 22 ( 4 ), 82-92 (Doi : https://doi.org/10.54216/IJNS.220407) |
| Chicago | A. Priya, P. Maragatha Meenakshi, Aiyared Iampan, N. Rajesh. "Neutrosophic nil radicals of neutrosophic ideals in rings." Journal of International Journal of Neutrosophic Science, 22 no. 4 (2023): 82-92 (Doi : https://doi.org/10.54216/IJNS.220407) |
| Harvard | A. Priya, P. Maragatha Meenakshi, Aiyared Iampan, N. Rajesh. (2023). Neutrosophic nil radicals of neutrosophic ideals in rings. Journal of International Journal of Neutrosophic Science, 22 ( 4 ), 82-92 (Doi : https://doi.org/10.54216/IJNS.220407) |
| Vancouver | A. Priya, P. Maragatha Meenakshi, Aiyared Iampan, N. Rajesh. Neutrosophic nil radicals of neutrosophic ideals in rings. Journal of International Journal of Neutrosophic Science, (2023); 22 ( 4 ): 82-92 (Doi : https://doi.org/10.54216/IJNS.220407) |
| IEEE | A. Priya, P. Maragatha Meenakshi, Aiyared Iampan, N. Rajesh, Neutrosophic nil radicals of neutrosophic ideals in rings, Journal of International Journal of Neutrosophic Science, Vol. 22 , No. 4 , (2023) : 82-92 (Doi : https://doi.org/10.54216/IJNS.220407) |