Abstract
Neutrosophic extended triplet group (NETG) is a novel algebra structure and it is different from the classical group. The major concern of this paper is to present the concept of a partially ordered neutrosophic extended triplet group (po-NETG), which is a NETG equipped with a partial order that relates to its multiplicative operation, and consider properties and structure features of po-NETGs. Firstly, in a po-NETG, we propose the concepts of the positive cone and negative cone, and investigate the structure features of them. Secondly, we study the specificity of the positive cone in a partially ordered weak commutative neutrosophic extended triplet group (po-WCNETG). Finally, we introduce the concept of a po-NETG homomorphism between two po-NETGs, construct a po-NETG on a quotient set by providing a multiplication and a partial order, then we discuss some fundamental properties of them.
Highlights
Groups play a very important role in algebraic structures [1,2,3], and have been applied in many other areas such as chemistry, physics, biology, etc
In this paper, inspired by the research work in algebraic structures equipped with a partial order, we proposed the concepts of po-neutrosophic extended triplet group (NETG), deeply studied the relationships between partially ordered neutrosophic extended triplet group (po-NETG) and their positive cones, and characterized the positive cone of a WCNETG after defining a partial order relation on it
By defining a special multiplication and a partial order on the quotient set, and we achieved the interrelation of homomorphisms and congruences of po-NETGs
Summary
College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China;.
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