On neutrosophic extended triplet groups (loops) and Abel-Grassmann's groupoids (AG-groupoids)
- Authors
- Zhang, Xiaohong; Wu, Xiaoying; Mao, Xiaoyan; Smarandache, Florentin; Park, Choonkil
- Issue Date
- Oct-2019
- Publisher
- IOS PRESS
- Keywords
- Semigroup; neutrosophic extended triplet group (NETG); completely regular semigroup; Clifford semigroup; Abel-Grassmann' s groupoid (AG-groupoid)
- Citation
- JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, v.37, no.4, pp.5743 - 5753
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF INTELLIGENT & FUZZY SYSTEMS
- Volume
- 37
- Number
- 4
- Start Page
- 5743
- End Page
- 5753
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/147004
- DOI
- 10.3233/JIFS-181742
- ISSN
- 1064-1246
- Abstract
- From the perspective of semigroup theory, the characterizations of a neutrosophic extended triplet group (NETG) and AG-NET-loop (which is both an Abel-Grassmann groupoid and a neutrosophic extended triplet loop) are systematically analyzed and some important results are obtained. In particular, the following conclusions are strictly proved: (1) an algebraic system is neutrosophic extended triplet group if and only if it is a completely regular semigroup; (2) an algebraic system is weak commutative neutrosophic extended triplet group if and only if it is a Clifford semigroup; (3) for any element in an AG-NET-loop, its neutral element is unique and idempotent; (4) every AG-NET-loop is a completely regular and fully regular Abel-Grassmann groupoid (AG-groupoid), but the inverse is not true. Moreover, the constructing methods of NETGs (completely regular semigroups) are investigated, and the lists of some finite NETGs and AG-NET-loops are given.
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