International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2615 2020 2020 Department of Mathematics, School of Science, University of Phayao, 19 Moo 2, Tambon Mae Ka, Amphur Mueang, Phayao 56000, Thailand Aiyared Aiyared Department of Mathematics, Rajah Serfoji Government College (affiliated to Bharathidasan University), Thanjavur 613005, Tamilnadu, India N. Rajesh The notion of neutrosophic N-deductive systems of Hilbert algebras is introduced, and several properties are investigated. Conditions for neutrosophic N-structures to be neutrosophic N-deductive systems of Hilbert algebras are provided. Relations between neutrosophic N-deductive systems and their level subsets are considered. The Cartesian product of neutrosophic N-structures is also supplied. Finally, we also find the property of the homomorphic pre-image of neutrosophic N-deductive systems. 2024 2024 358 368 10.54216/IJNS.230429 https://www.americaspg.com/articleinfo/21/show/2615