International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2202 2020 2020 Department of Mathematics, Government Arts College (affiliated to Bharathidasan University), Thanthonimalai, Karur 639005, Tamilnadu, India A. Priya Department of Mathematics, Thanthai Periyar Government Arts and Science College (affiliated to Bharathidasan University), Tiruchirappalli 624024, Tamilnadu, India P. Maragatha Meenakshi 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 Iampan Department of Mathematics, Rajah Serfoji Government College, Thanjavur 613005, Tamilnadu, India N. Rajesh 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]. 2023 2023 08 19 10.54216/IJNS.220401 https://www.americaspg.com/articleinfo/21/show/2202