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Mathematics 2019, 7(3), 268; https://doi.org/10.3390/math7030268

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

Department of Mathematics, Shaanxi University of Science &Technology, Xi’an 710021, China
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Received: 25 January 2019 / Revised: 7 March 2019 / Accepted: 8 March 2019 / Published: 15 March 2019
(This article belongs to the Special Issue General Algebraic Structures)
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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. View Full-Text
Keywords: neutrosophic extended triplet; Abel Grassmann’s groupoid; AG-NET-Loop; decomposition theorem; AG-(l, l)-Loop neutrosophic extended triplet; Abel Grassmann’s groupoid; AG-NET-Loop; decomposition theorem; AG-(l, l)-Loop
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Wu, X.; Zhang, X. The Decomposition Theorems of AG-Neutrosophic Extended Triplet Loops and Strong AG-(l, l)-Loops. Mathematics 2019, 7, 268.

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