This work is dedicated to give the reader a wide review for recent advantages in the algebraic study of neutrosophic matrices, refined neutrosophic matrices, and n-refined neutrosophic matrices.
This work is dedicated to study the conditions of diagonalization in the case of refined neutrosophic matrices, where it presents the necessary and sufficient conditions for the diagonalization of these matrices by finding a relationship with classical diagonalization of matrices. Also, it describes an algorithm to obtain all eigen values and eigen vectors of refined neutrosophic matrices from the classical ones.
Modules are one of the fundamental and rich algebraic structure concerning some binary operations in the study of algebra. In this paper, some basic structures of refined neutrosophic R-modules and refined neutrosophic submodules in algebra are generalized. Some properties of refined neutrosophic R-modules and refined neutrosophic submodules are presented. More precisely, classical modules and refined neutrosophic rings are utilized. Consequently, refinedneutrosophic R- modules that are completely different from the classical modular in the structural properties are introduced. Also, neutrosophic R-module homomorphism is explained and some definitions and theorems are presented.
The objective of this paper is to introduce a necessary and sufficient condition for a neutrosophic ring to be clean. This work proves the equivalence between case of classical clean ring and the corresponding neutrosophic ring ,refined neutrosophic ring , and n-refined neutrosophic ring .
In this study, we introduce the notion of special neutrosophic functions as new kinds of neutrosophic function defined in a neutrosophic logic. As particular cases, we present the notions of neutrosophic Floor (greatest integer), neutrosophic Absolute Function and neutrosophic Signum Function. Moreover, we draw its neutrosophic graph representation and discuss similarities and differences for these special neutrosophic functions between the classic case and neutrosophic case. We investigate some properties and prove them. However, we often need the definition of absolute value function, especially in the metric space. Therefore, we introduce its initial definition in this study.
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