International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2463 2020 2020 Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences (SIMATS), Chennai-602105, India G. Nisha Devi Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences (SIMATS), Chennai-602105, India P. Hemavathi Department of Mathematics, Prathyusha Engineering College (Autonomous), Thiruvallur-602025, India R. Vinodkumar Department of Mathematics, Muthurangam Government Arts College, Vellore-632002, India P. Muralikrishna Department of Mathematics, School of Science, University of Phayao, 19 Moo 2, Tambon Mae Ka, Amphur Mueang, Phayao 56000, Thailand Aiyared Iampan This study explores an innovative perspective on neutrosophic cubic Z-algebras, delving into the theoretical framework within mathematical structures. Through a comprehensive analysis, we uncover unique insights that contribute to the advancement of algebraic methodologies, particularly in handling uncertainties represented by neutrosophic elements. This work aims to present the idea of neutrosophic cubic sets in Z-algebras, as well as the usage of false membership function, truth, and indeterminacy in Z-algebras. Further, the results on -union, -intersection, -union, and -intersection of neutrosophic cubic Z-subalgebras are provided. This paper also discusses homomorphisms of Z-algebras and its associated characteristics. 2024 2024 77 86 10.54216/IJNS.230307 https://www.americaspg.com/articleinfo/21/show/2463