Deakin University
Browse

File(s) under permanent embargo

Commutative neutrosophic triplet group and neutro-homomorphism basic theorem

journal contribution
posted on 2018-07-01, 00:00 authored by X Zhang, F Smarandache, M Ali, X Liang
© 2018 Forum-Editrice Universitaria Udinese SRL. All rights reserved. Recently, the notions of neutrosophic triplet and neutrosophic triplet group are introduced by Florentin Smarandache and Mumtaz Ali. The neutrosophic triplet is a group of three elements that satisfy certain properties with some binary operations. The neutrosophic triplet group is completely different from the classical group in the structural properties. In this paper, we further study neutrosophic triplet group. First, to avoid confusion, some new symbols are introduced, and several basic properties of neutrosophic triplet group are rigorously proved (because the original proof is flawed), and a result about neutrosophic triplet subgroup is revised. Second, some new properties of commutative neutrosophic triplet group are funded, and a new equivalent relation is established. Third, based on the previous results, the following important propositions are proved: from any commutative neutrosophic triplet group, an Abel group can be constructed; from any commutative neutrosophic triplet group, a BCI-algebra can be constructed. Moreover, some important examples are given. Finally, by using any neutrosophic triplet subgroup of a commutative neutrosophic triplet group, a new congruence relation is established, and then the quotient structure induced by neutrosophic triplet subgroup is constructed and the neutro-homomorphism basic theorem is proved.

History

Journal

Italian journal of pure and applied mathematics

Issue

40

Pagination

353 - 375

Publisher

Forum Editrice Universitaria Udinese

Location

Udine, Italy

ISSN

1126-8042

eISSN

2239-0227

Language

eng

Publication classification

C1.1 Refereed article in a scholarly journal

Copyright notice

2018, Forum Editrice Universitaria Udinese

Usage metrics

    Research Publications

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC