The innovative notion of neutrosophic triplet groups, introduced by Smarandache and Ali in 2014-2016, happens to yield the anti-element and neutral element once the element is given. It is established that the neutrosophic triplet group collection forms the classical group under product for Zn, for some specific n. However the collection is not even closed under sum. These neutrosophic triplet groups are built using only modulo integers or Cayley tables. Several interesting properties related with them are defined. It is pertinent to record that in Zn, when n is a prime number, we cannot get a neutral element which can contribute to nontrivial neutrosophic triplet groups. Further, all neutral elements in Zn are only nontrivial idempotents. Using neutrosophic triplet groups authors have defined the notion of neutrosophic triplet group matrices.
EuropaNova ASBL, Brussels
neutrosophic triplet group, algebra, neutrosophic logic
W.B. Vasantha Kandasamy, Ilanthenral K, F. Smarandache (eds.) Neutrosophic Triplet Groups and their Applications to Mathematical Modelling. Brussels: EuropaNova ASBL, 2017
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