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International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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International Journal of Neutrosophic Science

Volume 22 , Issue 4 , PP: 08-19, 2023 | Cite this article as | XML | Html | PDF | Full Length Article

Polynomial ideals of a ring based on neutrosophic sets

A. Priya 1 * , P. Maragatha Meenakshi 2 , Aiyared Iampan 3 , N. Rajesh 4

  • 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)

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

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

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    [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.

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

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