Neutrosophic Triplets in Neutrosophic Rings

Vasantha Kandasamy W. B., Ilanthenral Kandasamy and Florentin Smarandache
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Vasantha Kandasamy W. B.: School of Computer Science and Engineering, VIT, Vellore 632014, India
Ilanthenral Kandasamy: School of Computer Science and Engineering, VIT, Vellore 632014, India
Florentin Smarandache: Department of Mathematics, University of New Mexico, 705 Gurley Avenue, Gallup, NM 87301, USA

Mathematics, 2019, vol. 7, issue 6, 1-9

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.

Keywords: neutrosophic ring; neutrosophic triplets; idemponents; special neutrosophic triplets (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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