On neutrosophic extended triplet groups (loops) and Abel-Grassmann’s groupoids (AG-groupoids) PDF Download

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On neutrosophic extended triplet groups (loops) and Abel-Grassmann’s groupoids (AG-groupoids)

On neutrosophic extended triplet groups (loops) and Abel-Grassmann’s groupoids (AG-groupoids) PDF Author: Xiaohong Zhang
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 11

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Book Description
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.