Left (Right)-Quasi Neutrosophic Triplet Loops (Groups) and Generalized BE-Algebras
1
Department of Mathematics, Shaanxi University of Science & Technology, Xi’an 710021, China
2
Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China
3
Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(7), 241; https://doi.org/10.3390/sym10070241
Received: 29 May 2018 / Revised: 12 June 2018 / Accepted: 19 June 2018 / Published: 26 June 2018
(This article belongs to the Special Issue Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets)
The new notion of a neutrosophic triplet group (NTG) is proposed by Florentin Smarandache; it is a new algebraic structure different from the classical group. The aim of this paper is to further expand this new concept and to study its application in related logic algebra systems. Some new notions of left (right)-quasi neutrosophic triplet loops and left (right)-quasi neutrosophic triplet groups are introduced, and some properties are presented. As a corollary of these properties, the following important result are proved: for any commutative neutrosophic triplet group, its every element has a unique neutral element. Moreover, some left (right)-quasi neutrosophic triplet structures in BE-algebras and generalized BE-algebras (including CI-algebras and pseudo CI-algebras) are established, and the adjoint semigroups of the BE-algebras and generalized BE-algebras are investigated for the first time.
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Keywords:
neutrosophic triplet; quasi neutrosophic triplet loop; quasi neutrosophic triplet group; BE-algebra; CI-algebra
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
MDPI and ACS Style
Zhang, X.; Wu, X.; Smarandache, F.; Hu, M. Left (Right)-Quasi Neutrosophic Triplet Loops (Groups) and Generalized BE-Algebras. Symmetry 2018, 10, 241.
AMA Style
Zhang X, Wu X, Smarandache F, Hu M. Left (Right)-Quasi Neutrosophic Triplet Loops (Groups) and Generalized BE-Algebras. Symmetry. 2018; 10(7):241.
Chicago/Turabian StyleZhang, Xiaohong; Wu, Xiaoying; Smarandache, Florentin; Hu, Minghao. 2018. "Left (Right)-Quasi Neutrosophic Triplet Loops (Groups) and Generalized BE-Algebras" Symmetry 10, no. 7: 241.
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