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International Journal of Neutrosophic Science

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Online: 2690-6805 Print: 2692-6148
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International Journal of Neutrosophic Science
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Volume 22 • Issue 4 • PP: 08-19 • 2023

Polynomial ideals of a ring based on neutrosophic sets

A. Priya 1*
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,
P. Maragatha Meenakshi 2
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,
Aiyared Iampan 3
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,
N. Rajesh 4
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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
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© 2023 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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

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

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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
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