International Journal of Neutrosophic Science

The objective of this paper is to study some novel algebraic properties of neutrosophic matrices. Also, this work introduces the concept of neutrosophic characteristic polynomial of a square neutrosophic matrix and the neutrosophic version of Cayley-Hamilton.On the other hand, we illustrate many examples about the validity of this work.

This paper is dedicated to study the group of units problem in some 2-cyclic refined neutrosophic rings, where it presents a full classification of the group of units in 2-cyclic refined neutrosophic ring of integers  , 2-cyclic refined neutrosophic ring of integers modulo 2 and 3 ,  and 2-cyclic refined neutrosophic ring of real numbers , as direct products of the cyclic groups. On the other hand, this work provides a necessary and sufficient condition for the invertibility of any square 2-cyclic refined neutrosophic real matrix. Also, we will illustrate some examples to clarify the validity of our work.

The aim of this article is to investigate a new kind of Neutrosophic open and closed mappings called quasi N g#− Open and quasi N g#− closed mappings and analyse their characterizations in Neutrosophic topolog-ical spaces with necessary examples.

In this article, the concept of N-neutrosophic crisp γ-open and N-neutrosophic crisp γ-closed mappings in N-neutrosophic crisp topological spaces are introduced and studied some of their related properties. Also, Nneutrosophic crisp γ irresolute mapping is introduced in N-neutrosophic crisp topological spaces. Further, it is extended to N-neutrosophic crisp γ-homeomorphism, N-neutrosophic crisp γ-Completely homeomorphism and N-neutrosophic crisp γT1/2-space in N-neutrosophic crisp topological spaces and establishes some of their related properties. Finally, Strongly N-neutrosophic crisp γ continuous and Perfectly N-neutrosophic crisp γ continuous functions is also discuss.

Recently, a problem is addressed about dealing the difference among Non-Euclidean, AntiGeometry and NeutroGeoemtry data sets. The problem arises while partial negation of Euclidean Geometry, full negation of Euclidean or Hybrid mode. In case of undefined geometry also many researchers raised the questions. To tackle this issue, the current paper provides some examples for Non-Euclidean, AntiGeometry, and Neutrogemoetry for better understanding.