1 Affiliation : School of Computer Science and Engineering, Vellore Institute of Technology, Vellore, Tamil Nadu, India
Email : vasantha.wb@vit.ac.in
2 Affiliation : School of Computer Science and Engineering, Vellore Institute of Technology, Vellore, Tamil Nadu, India
Email : ilanthenral.k@vit.ac.in
3 Affiliation : Dept. Math and Sciences, University of New Mexico, Gallup, NM, USA
Email : smarand@unm.edu
Abstract :
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.
Keywords :
NeutroAlgebra , AntiAlgebra , groupring , NeutrosubAlgebra , Partial Algebra , groups , ideals , Smarandache semigroup.
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Received: Month Day, Year. Accepted: Month Day, Year
| Style | # |
|---|---|
| MLA | Vasantha Kandasamy ,Ilanthenral Kandasamy,Florentin Smarandache. "NeutroAlgebra of Substructures of the Semigroups built using Zn and Z+." International Journal of Neutrosophic Science, Vol. 18, No. 3, 2022 ,PP. 135-156. |
| APA | Vasantha Kandasamy ,Ilanthenral Kandasamy,Florentin Smarandache. (2022). NeutroAlgebra of Substructures of the Semigroups built using Zn and Z+. International Journal of Neutrosophic Science, 18 ( 3 ), 135-156. |
| Chicago | Vasantha Kandasamy ,Ilanthenral Kandasamy,Florentin Smarandache. "NeutroAlgebra of Substructures of the Semigroups built using Zn and Z+." International Journal of Neutrosophic Science, 18 no. 3 (2022): 135-156. |
| Harvard | Vasantha Kandasamy ,Ilanthenral Kandasamy,Florentin Smarandache. (2022). NeutroAlgebra of Substructures of the Semigroups built using Zn and Z+. International Journal of Neutrosophic Science, 18 ( 3 ), 135-156. |
| Vancouver | Vasantha Kandasamy ,Ilanthenral Kandasamy,Florentin Smarandache. NeutroAlgebra of Substructures of the Semigroups built using Zn and Z+. International Journal of Neutrosophic Science, (2022); 18 ( 3 ): 135-156. |
| IEEE | Vasantha Kandasamy,Ilanthenral Kandasamy,Florentin Smarandache, NeutroAlgebra of Substructures of the Semigroups built using Zn and Z+, International Journal of Neutrosophic Science, Vol. 18 , No. 3 , (2022) : 135-156 (Doi : https://doi.org/10.54216/IJNS.1803012) |