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Neutrosophic Triplets in Neutrosophic Rings

Author

Listed:
  • 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)

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.

Suggested Citation

  • Vasantha Kandasamy W. B. & Ilanthenral Kandasamy & Florentin Smarandache, 2019. "Neutrosophic Triplets in Neutrosophic Rings," Mathematics, MDPI, vol. 7(6), pages 1-9, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:563-:d:241669
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