Abstract
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.
Highlights
IntroductionHandling of indeterminacy present in real world data is introduced in [1,2] as neutrosophy
Handling of indeterminacy present in real world data is introduced in [1,2] as neutrosophy.Neutralities and indeterminacies represented by Neutrosophic logic has been used in analysis of real world and engineering problems [3,4,5].Neutrosophic algebraic structures such as neutrosophic rings, groups and semigroups are presented and analyzed and their application to fuzzy and neutrosophic models are developed in [6]
We for the first time completely characterize neutrosophic triplets in neutrosophic rings. We prove this collection of neutrosophic triplets using neutrosophic rings are not even closed under addition. We prove that they form a torsion free abelian group under component wise multiplication
Summary
Handling of indeterminacy present in real world data is introduced in [1,2] as neutrosophy. Neutralities and indeterminacies represented by Neutrosophic logic has been used in analysis of real world and engineering problems [3,4,5]. Neutrosophic algebraic structures such as neutrosophic rings, groups and semigroups are presented and analyzed and their application to fuzzy and neutrosophic models are developed in [6]. Neutrosophic triplets in the case of neutrosophic rings have not yet been researched. We prove that they form a torsion free abelian group under component wise multiplication
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