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Symmetry in Hyperstructure: Neutrosophic Extended Triplet Semihypergroups and Regular Hypergroups
Open AccessArticle

The Structure of Idempotents in Neutrosophic Rings and Neutrosophic Quadruple Rings

1
School of Science, Xi’an Polytechnic University, Xi’an 710048, China
2
School of Arts and Sciences, Shaanxi University of Science & Technology, Xi’an 710021, China
3
Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(10), 1254; https://doi.org/10.3390/sym11101254
Received: 12 September 2019 / Revised: 4 October 2019 / Accepted: 5 October 2019 / Published: 8 October 2019
This paper aims to reveal the structure of idempotents in neutrosophic rings and neutrosophic quadruple rings. First, all idempotents in neutrosophic rings R I are given when R is C , R , Q , Z or Z n . Secondly, the neutrosophic quadruple ring R T I F is introduced and all idempotents in neutrosophic quadruple rings C T I F , R T I F , Q T I F , Z T I F and Z n T I F are also given. Furthermore, the algorithms for solving the idempotents in Z n I and Z n T I F for each nonnegative integer n are provided. Lastly, as a general result, if all idempotents in any ring R are known, then the structure of idempotents in neutrosophic ring R I and neutrosophic quadruple ring R T I F can be determined. View Full-Text
Keywords: neutrosophic rings; neutrosophic quadruple rings; idempotents; neutrosophic extended triplet group; neutrosophic set neutrosophic rings; neutrosophic quadruple rings; idempotents; neutrosophic extended triplet group; neutrosophic set
MDPI and ACS Style

Ma, Y.; Zhang, X.; Smarandache, F.; Zhang, J. The Structure of Idempotents in Neutrosophic Rings and Neutrosophic Quadruple Rings. Symmetry 2019, 11, 1254.

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