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Full Length Article
International Journal of Neutrosophic Science
Volume 18 , Issue 3, PP: 135-156 , 2022 | Cite this article as | XML | Html |PDF

Title

NeutroAlgebra of Substructures of the Semigroups built using Zn and Z+

Authors Names :   Vasantha Kandasamy   1 *     Ilanthenral Kandasamy   2     Florentin Smarandache   3  

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



Doi   :   https://doi.org/10.54216/IJNS.1803012

Received: February 05, 2022 Accepted: April 23, 2022

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


Cite this Article as :
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)