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Generalized Abel-Grassmann’s Neutrosophic Extended Triplet Loop

Author

Listed:
  • Xiaogang An

    (School of Arts and Sciences, Shaanxi University of Science & Technology, Xi’an 710021, China)

  • Xiaohong Zhang

    (School of Arts and Sciences, Shaanxi University of Science & Technology, Xi’an 710021, China)

  • Yingcang Ma

    (School of Science, Xi’an Polytechnic University, Xi’an 710048, China)

Abstract

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.

Suggested Citation

  • Xiaogang An & Xiaohong Zhang & Yingcang Ma, 2019. "Generalized Abel-Grassmann’s Neutrosophic Extended Triplet Loop," Mathematics, MDPI, vol. 7(12), pages 1-20, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1206-:d:295758
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    References listed on IDEAS

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    1. Protić, P.V. & Stevanović, N., 1995. "AG-test and some general properties of Abel-Grassmann's groupoids," Pure Mathematics and Applications, Department of Mathematics, Corvinus University of Budapest, vol. 6(4), pages 371-383.
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    Cited by:

    1. Minghao Hu & Xiaohong Zhang, 2022. "On Cyclic Associative Semihypergroups and Neutrosophic Extended Triplet Cyclic Associative Semihypergroups," Mathematics, MDPI, vol. 10(4), pages 1-30, February.

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