Study Of Two Kinds Of Quasi Ag Neutrosophic Extended Triplet Loops
Download Study Of Two Kinds Of Quasi Ag Neutrosophic Extended Triplet Loops PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Study Of Two Kinds Of Quasi Ag Neutrosophic Extended Triplet Loops book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Study of Two Kinds of Quasi AG-Neutrosophic Extended Triplet Loops
Abel-Grassmann’s groupoid and neutrosophic extended triplet loop are two important algebraic structures that describe two kinds of generalized symmetries. In this paper, we investigate quasi AG-neutrosophic extended triplet loop, which is a fusion structure of the two kinds of algebraic structures mentioned above.
Generalized Abel-Grassmann’s Neutrosophic Extended Triplet Loop
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.
On neutrosophic extended triplet groups (loops) and Abel-Grassmann’s groupoids (AG-groupoids)
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.