Polynomial ideals of a ring based on neutrosophic sets

A.; P. Maragatha; Aiyared; N.

doi:https://doi.org/10.54216/IJNS.220401

Full Length Article

Volume 22 • Issue 4 • PP: 08-19 • 2023

Polynomial ideals of a ring based on neutrosophic sets

A. Priya ^1*

mail

,

P. Maragatha Meenakshi ²

mail

,

Aiyared Iampan ³

mail

,

N. Rajesh ⁴

mail

¹Department of Mathematics, Government Arts College (affiliated to Bharathidasan University), Thanthonimalai, Karur 639005, Tamilnadu, India

²Department of Mathematics, Thanthai Periyar Government Arts and Science College (affiliated to Bharathidasan University), Tiruchirappalli 624024, Tamilnadu, India

³Fuzzy Algebras and Decision-Making Problems Research Unit, School of Science, University of Phayao, 19 Moo 2, Tambon Mae Ka, Amphur Mueang, Phayao 56000, Thailand

⁴Department of Mathematics, Rajah Serfoji Government College, Thanjavur 613005, Tamilnadu, India

* Corresponding Author.

DOI https://doi.org/10.54216/IJNS.220401

format_quote Cite this article

Received: May 12, 2023 Revised: July 07, 2023 Accepted: November 01, 2023

View PDF open_in_new

Abstract

In this paper, we introduce the notion of the neutrosophic polynomial ideal Ax of a polynomial ring R[x] induced by a neutrosophic ideal A of a ring R and obtain an isomorphism theorem of a ring of neutrosophic cosets of Ax. It is shown that a neutrosophic ideal A of a ring is a neutrosophic prime if and only if Ax is a neutrosophic prime ideal of R[x].

Keywords

neutrosophic ideal neutrosophic prime ideal neutrosophic polynomial ideal f-invariant.

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] 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.

[6] 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.

[7] 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.

[8] F. Smarandache, A unifying field in logics: neutrosophic logic, neutrosophy, neutrosophic set, neutrosophic probability, American Research Press, Rehoboth, New Mexico, (1999).

[9] L. A. Zadeh, Fuzzy sets, Information and control, 8(3), (1965), 338-353.

Cite This Article

Choose your preferred format

format_quote

Priya, A., Meenakshi, P. Maragatha, Iampan, Aiyared, Rajesh, N.. "Polynomial ideals of a ring based on neutrosophic sets." International Journal of Neutrosophic Science, vol. Volume 22, no. Issue 4, 2023, pp. 08-19. DOI: https://doi.org/10.54216/IJNS.220401

Priya, A., Meenakshi, P., Iampan, A., Rajesh, N. (2023). Polynomial ideals of a ring based on neutrosophic sets. International Journal of Neutrosophic Science, Volume 22(Issue 4), 08-19. DOI: https://doi.org/10.54216/IJNS.220401

Priya, A., Meenakshi, P. Maragatha, Iampan, Aiyared, Rajesh, N.. "Polynomial ideals of a ring based on neutrosophic sets." International Journal of Neutrosophic Science Volume 22, no. Issue 4 (2023): 08-19. DOI: https://doi.org/10.54216/IJNS.220401

Priya, A., Meenakshi, P., Iampan, A., Rajesh, N. (2023) 'Polynomial ideals of a ring based on neutrosophic sets', International Journal of Neutrosophic Science, Volume 22(Issue 4), pp. 08-19. DOI: https://doi.org/10.54216/IJNS.220401

Priya A, Meenakshi P, Iampan A, Rajesh N. Polynomial ideals of a ring based on neutrosophic sets. International Journal of Neutrosophic Science. 2023;Volume 22(Issue 4):08-19. DOI: https://doi.org/10.54216/IJNS.220401

A. Priya, P. Meenakshi, A. Iampan, N. Rajesh, "Polynomial ideals of a ring based on neutrosophic sets," International Journal of Neutrosophic Science, vol. Volume 22, no. Issue 4, pp. 08-19, 2023. DOI: https://doi.org/10.54216/IJNS.220401

Digital Archive Ready