Abstract
The new notion of a neutrosophic triplet group (NTG) is proposed by Florentin Smarandache; it is a new algebraic structure different from the classical group. The aim of this paper is to further expand this new concept and to study its application in related logic algebra systems. Some new notions of left (right)-quasi neutrosophic triplet loops and left (right)-quasi neutrosophic triplet groups are introduced, and some properties are presented. As a corollary of these properties, the following important result are proved: for any commutative neutrosophic triplet group, its every element has a unique neutral element. Moreover, some left (right)-quasi neutrosophic triplet structures in BE-algebras and generalized BE-algebras (including CI-algebras and pseudo CI-algebras) are established, and the adjoint semigroups of the BE-algebras and generalized BE-algebras are investigated for the first time.
Highlights
The symmetry exists in the real world, and group theory is a mathematical tool for describing symmetry
Smarandache [5,6] introduced another new algebraic structure, namely: neutrosophic triplet group, which comes from the theory of the neutrosophic set
We introduce various general neutrosophic triplet structures, such as (l-l)-type, (l-r)-type, (r-l)-type, (r-r)-type, (l-lr)-type, (r-lr)-type,type, and-type quasi neutrosophic triplet loops, and investigate their basic properties
Summary
The symmetry exists in the real world, and group theory is a mathematical tool for describing symmetry. As a new extension of the concept of group, the neutrosophic triplet group has attracted the attention of many scholars, and a series of related papers have been published [12,13,14,15]. Similar to BCI-algebra as a generalization of BCK-algebra, B.L. Meng introduced the concept of CI-algebra, which is as a generalization of BE-algebra, and studied the structures and closed filters of CI-algebras [35,36,37]. We introduce various general neutrosophic triplet structures, such as (l-l)-type, (l-r)-type, (r-l)-type,. We further study the properties of (pseudo) BE-algebras and (pseudo) CI-algebras, and the general neutrosophic triplet structures that are contained in a BE-algebra (CI-algebra) and pseudo. For the first time, we introduce the concepts of adjoint semigroups of BE-algebras and generalized BE-algebras (including CI-algebras, pseudo BE-algebras, and pseudo CI-algebras) and discuss some interesting topics
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