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International Journal of Neutrosophic Science
Volume 22 , Issue 4, PP: 08-19 , 2023 | Cite this article as | XML | Html |PDF

Title

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)

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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 :

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Cite this Article as :
Style #
MLA A. Priya, P. Maragatha Meenakshi, Aiyared Iampan, N. Rajesh. "Polynomial ideals of a ring based on neutrosophic sets." International Journal of Neutrosophic Science, Vol. 22, No. 4, 2023 ,PP. 08-19 (Doi   :  https://doi.org/10.54216/IJNS.220401)
APA A. Priya, P. Maragatha Meenakshi, Aiyared Iampan, N. Rajesh. (2023). Polynomial ideals of a ring based on neutrosophic sets. Journal of International Journal of Neutrosophic Science, 22 ( 4 ), 08-19 (Doi   :  https://doi.org/10.54216/IJNS.220401)
Chicago A. Priya, P. Maragatha Meenakshi, Aiyared Iampan, N. Rajesh. "Polynomial ideals of a ring based on neutrosophic sets." Journal of International Journal of Neutrosophic Science, 22 no. 4 (2023): 08-19 (Doi   :  https://doi.org/10.54216/IJNS.220401)
Harvard A. Priya, P. Maragatha Meenakshi, Aiyared Iampan, N. Rajesh. (2023). Polynomial ideals of a ring based on neutrosophic sets. Journal of International Journal of Neutrosophic Science, 22 ( 4 ), 08-19 (Doi   :  https://doi.org/10.54216/IJNS.220401)
Vancouver A. Priya, P. Maragatha Meenakshi, Aiyared Iampan, N. Rajesh. Polynomial ideals of a ring based on neutrosophic sets. Journal of International Journal of Neutrosophic Science, (2023); 22 ( 4 ): 08-19 (Doi   :  https://doi.org/10.54216/IJNS.220401)
IEEE A. Priya, P. Maragatha Meenakshi, Aiyared Iampan, N. Rajesh, Polynomial ideals of a ring based on neutrosophic sets, Journal of International Journal of Neutrosophic Science, Vol. 22 , No. 4 , (2023) : 08-19 (Doi   :  https://doi.org/10.54216/IJNS.220401)
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