Neutrosophic Duplets of {Zpn,×} and {Zpq,×} and Their Properties

Kandasamy W.B., Vasantha; Kandasamy, Ilanthenral; Smarandache, Florentin

doi:10.3390/sym10080345

Volume 10, Issue 8

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Symmetry 2018, 10(8), 345; https://doi.org/10.3390/sym10080345

Neutrosophic Duplets of {Z_pn,×} and {Z_pq,×} and Their Properties

Vasantha Kandasamy W.B.¹

, Ilanthenral Kandasamy^1,*

and Florentin Smarandache²

School of Computer Science and Engineering, VIT, Vellore 632014, India

Department of Mathematics, University of New Mexico, 705 Gurley Avenue, Gallup, NM 87301, USA

Author to whom correspondence should be addressed.

Received: 31 July 2018 / Revised: 13 August 2018 / Accepted: 15 August 2018 / Published: 17 August 2018

(This article belongs to the Special Issue Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets)

Full-Text | PDF [720 KB, uploaded 17 August 2018]

Abstract

The notions of neutrosophy, neutrosophic algebraic structures, neutrosophic duplet and neutrosophic triplet were introduced by Florentin Smarandache. In this paper, the neutrosophic duplets of

Z_{p^{n}}

Z_{p q}

and

Z_{p_{1} p_{2} \dots p_{n}}

are studied. In the case of

Z_{p^{n}}

and

Z_{p q}

, the complete characterization of neutrosophic duplets are given. In the case of

Z_{p_{1} \dots p_{n}}

, only the neutrosophic duplets associated with

p_{i}

s are provided;

i = 1, 2, \dots, n

. Some open problems related to neutrosophic duplets are proposed. View Full-Text

Keywords: neutrosophic duplets; semigroup; neutrosophic triplet groups

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).