International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/1071 2020 2020 School of Computer Science and Engineering, Vellore Institute of Technology, Vellore, Tamil Nadu, India Vasantha .. School of Computer Science and Engineering, Vellore Institute of Technology, Vellore, Tamil Nadu, India Ilanthenral Kandasamy Dept. Math and Sciences, University of New Mexico, Gallup, NM, USA Florentin Smarandache For the first-time authors study the NeutroAlgebraic structures of the substructures of the semigroups, { , ×}, { , ×} and { , +} where  = {1, 2, …, ¥}. The three substructures of the semigroup studied in the context of NeutroAlgebra are subsemigroups, ideals and groups. The substructure group has meaning only if the semigroup under consideration is a Smarandache semigroup. Further in this paper, all semigroups are only commutative. It is proved the NeutroAlgebraic structure of ideals (and subsemigroups) of a semigroup can be AntiAlgebra or NeutroAlgebra in the case of infinite semigroups built on  or  =   È {0}. However, in the case of S = { , ×}; n a composite number, S is always a Smarandache semigroup. The substructures of them are completely analyzed. Further groups of Smarandache semigroups can only be a NeutroAlgebra and never an AntiAlgebra. Open problems are proposed in the final section for researchers interested in this field of study. 2022 2022 135 156 10.54216/IJNS.1803012 https://www.americaspg.com/articleinfo/21/show/1071