Affiliations: [a] Department of Mathematics, Shaanxi University of Science & Technology, Xi’an, China
| [b] Department of Mathematics, Shanghai Maritime University, Shanghai, China
| [c] College of Science and Technology, Ningbo University, Ningbo, China
| [d] Department of Mathematics, University of New Mexico, Gallup, NM, USA
| [e] Department of Mathematics, Hanyang University, Seoul, Korea
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.
