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

Xiaoying Wu and Xiaohong Zhang
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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

Mathematics, 2019, vol. 7, issue 3, 1-13

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.

Keywords: neutrosophic extended triplet; Abel Grassmann’s groupoid; AG-NET-Loop; decomposition theorem; AG-( l , l )-Loop (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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