Volume 18 , Issue 3 , PP: 135-156, 2022 | Cite this article as | XML | Html | PDF | Full Length Article
Vasantha Kandasamy 1 * , Ilanthenral Kandasamy 2 , Florentin Smarandache 3
Doi: https://doi.org/10.54216/IJNS.1803012
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.
NeutroAlgebra, AntiAlgebra, groupring, NeutrosubAlgebra, Partial Algebra, groups, ideals, Smarandache semigroup. ,
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Received: Month Day, Year. Accepted: Month Day, Year
