aspg-21-2463-1791475484 20261008160444 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2024 23 3 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, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences (SIMATS), Chennai-602105, India R. Vinodkumar Department of Mathematics, Prathyusha Engineering College (Autonomous), Thiruvallur-602025, India P. Muralikrishna Department of Mathematics, Muthurangam Government Arts College, Vellore-632002, India Aiyared Iampan Department of Mathematics, School of Science, University of Phayao, 19 Moo 2, Tambon Mae Ka, Amphur Mueang, Phayao 56000, Thailand 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 style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman"'> m:val="script"/>S -union, style='font-size:10.0pt;font-family:"Cambria Math",serif;mso-bidi-font-family: "Times New Roman"'>S -intersection, style='font-size:10.0pt;font-family:"Cambria Math",serif;mso-fareast-font-family: "Times New Roman";mso-fareast-theme-font:minor-fareast;mso-bidi-font-family: "Times New Roman"'>K -union, and normal'> mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast; mso-bidi-font-family:"Times New Roman"'> m:val="i"/>K -intersection of neutrosophic cubic Z-subalgebras are provided. This paper also discusses homomorphisms of Z-algebras and its associated characteristics. 2024 77 86 2463 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.230307 https://www.americaspg.com/journal/21/article/2463 https://www.americaspg.com/storage/81706638825.pdf