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Open AccessArticle

Generalized Abel-Grassmann’s Neutrosophic Extended Triplet Loop

1
School of Arts and Sciences, Shaanxi University of Science & Technology, Xi’an 710021, China
2
School of Science, Xi’an Polytechnic University, Xi’an 710048, China
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1206; https://doi.org/10.3390/math7121206
Received: 5 November 2019 / Revised: 2 December 2019 / Accepted: 4 December 2019 / Published: 9 December 2019
(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)
A group is an algebraic system that characterizes symmetry. As a generalization of the concept of a group, semigroups and various non-associative groupoids can be considered as algebraic abstractions of generalized symmetry. In this paper, the notion of generalized Abel-Grassmann’s neutrosophic extended triplet loop (GAG-NET-Loop) is proposed and some properties are discussed. In particular, the following conclusions are strictly proved: (1) an algebraic system is an AG-NET-Loop if and only if it is a strong inverse AG-groupoid; (2) an algebraic system is a GAG-NET-Loop if and only if it is a quasi strong inverse AG-groupoid; (3) an algebraic system is a weak commutative GAG-NET-Loop if and only if it is a quasi Clifford AG-groupoid; and (4) a finite interlaced AG-(l,l)-Loop is a strong AG-(l,l)-Loop. View Full-Text
Keywords: Abel-Grassmann’s neutrosophic extended triplet loop; generalized Abel-Grassmann’s neutrosophic extended triplet loop; strong inverse AG-groupoid; quasi strong inverse AG-groupoid; quasi Clifford AG-groupoid Abel-Grassmann’s neutrosophic extended triplet loop; generalized Abel-Grassmann’s neutrosophic extended triplet loop; strong inverse AG-groupoid; quasi strong inverse AG-groupoid; quasi Clifford AG-groupoid
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MDPI and ACS Style

An, X.; Zhang, X.; Ma, Y. Generalized Abel-Grassmann’s Neutrosophic Extended Triplet Loop. Mathematics 2019, 7, 1206.

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