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The Decomposition Theorems of AG-Neutrosophic Extended Triplet Loops and Strong AG-( l , l )-Loops

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  • Xiaoying Wu

    (Department of Mathematics, Shaanxi University of Science &Technology, Xi’an 710021, China)

  • Xiaohong Zhang

    (Department of Mathematics, Shaanxi University of Science &Technology, Xi’an 710021, China)

Abstract

In this paper, some new properties of Abel Grassmann‘s Neutrosophic Extended Triplet Loop (AG-NET-Loop) were further studied. The following important results were proved: (1) an AG-NET-Loop is weakly commutative if, and only if, it is a commutative neutrosophic extended triplet (NETG); (2) every AG-NET-Loop is the disjoint union of its maximal subgroups. At the same time, the new notion of Abel Grassmann’s ( l , l )-Loop (AG-( l , l )-Loop), which is the Abel-Grassmann’s groupoid with the local left identity and local left inverse, were introduced. The strong AG-( l , l )-Loops were systematically analyzed, and the following decomposition theorem was proved: every strong AG-( l , l )-Loop is the disjoint union of its maximal sub-AG-groups.

Suggested Citation

  • Xiaoying Wu & Xiaohong Zhang, 2019. "The Decomposition Theorems of AG-Neutrosophic Extended Triplet Loops and Strong AG-( l , l )-Loops," Mathematics, MDPI, vol. 7(3), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:268-:d:214325
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    References listed on IDEAS

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    1. Qaiser Mushtaq & M. S. Kamran, 2001. "Finite AG-groupoid with left identity and left zero," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 27, pages 1-3, January.
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    Cited by:

    1. Songtao Shao & Xiaohong Zhang, 2019. "Measures of Probabilistic Neutrosophic Hesitant Fuzzy Sets and the Application in Reducing Unnecessary Evaluation Processes," Mathematics, MDPI, vol. 7(7), pages 1-23, July.
    2. Vasantha Kandasamy W.B. & Ilanthenral Kandasamy & Florentin Smarandache, 2019. "Neutrosophic Quadruple Vector Spaces and Their Properties," Mathematics, MDPI, vol. 7(8), pages 1-8, August.
    3. 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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