Conjectures for Invertible Diophantine Equations Of 3-Cyclic and 4-Cyclic Refined Integers

Abstract

The objective of this paper is to suggest two new conjectures concerning the invertible elements in 3-cyclic, and 4-cyclic refined neutrosophic rings of integers, where the invertibility condition shows that the solution of some Diophantine equations may determine the classification of the group of units of these algebraic rings.

On Novel Results about the Algebraic Properties of Symbolic 3-Plithogenic and 4-Plithogenic Real Square Matrices

“…Symbolic 2-plithogenic matrices were defined and studied in [14]; these matrices consist of symbolic 2-plithogenic real entries. These matrices are recognized as a similar structure of refined neutrosophic matrices and structures [15][16][17][18][19][20][21][22][23][24]. In matrix theory, it is very important to deal with the exponents of matrices and their related problems, such as how to diagonalize a matrix, and how to compute eigenvalues and eigenvectors.…”