Neutrosophic Triplets in Neutrosophic Rings

The neutrosophic triplets in neutrosophic rings ⟨ Q ∪ I ⟩ and ⟨ R ∪ I ⟩ are investigated in this paper. However, non-trivial neutrosophic triplets are not found in ⟨ Z ∪ I ⟩ . In the neutrosophic ring of integers Z \ { 0 , 1 } , no element has inverse in Z. It is proved that these rings can contain only three types of neutrosophic triplets, these collections are distinct, and these collections form a torsion free abelian group as triplets under component wise product. However, these collections are not even closed under component wise addition.