Generalized Abel-Grassmann’s Neutrosophic Extended Triplet Loop

Xiaogang An, Xiaohong Zhang and Yingcang Ma
Additional contact information
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

Mathematics, 2019, vol. 7, issue 12, 1-20

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.

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 (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 (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/12/1206/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/12/1206/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:12:p:1206-:d:295758

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().