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- Title
NeutroAlgebra of Substructures of the Semigroups built using Z<sub>n</sub> and Z<sup>+</sup>.
- Authors
Kandasamy, Vasantha; Kandasamy, Ilanthenral; Smarandache, Florentin
- Abstract
For the first-time authors study the NeutroAlgebraic structures of the substructures of the semigroups, { n Z, ×}, {Z, ×} and {Z, +} where Z = {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 Z or Z* = Z {0}. However, in the case of S = { n Z, ×}; 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.
- Subjects
SEMIGROUPS (Algebra); PARTIAL algebras; PROBLEM solving; MATHEMATICAL models; MATHEMATICAL analysis
- Publication
International Journal of Neutrosophic Science (IJNS), 2022, Vol 18, Issue 3, p135
- ISSN
2692-6148
- Publication type
Article
- DOI
10.54216/IJNS.1803012