A Study Of Some Neutrosophic Clean Rings

Abstract

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 .

On Clean and Nil-clean Symbolic 2-Plithogenic Rings

“…In [18], H. Suryoto and T. Uidjiani studied the concept of neutrosophic clean ring with many elementary interesting properties. Recently, M. Abobala [6], proved that a neutrosophic ring R(I) is clean if and only if R is clean. Motivated by this works, in this paper we have introduced and studied the notion of clean and nil-clean symbolic 2-plithogenic rings.…”

On the Classification of n-Refined Neutrosophic Rings and Its Applications in Matrix Computing Algorithms and Linear Systems

“…Neutrosophic logic as a new branch of mathematical philosophy has an impact in many fields of human knowledge. We see a lot of applications of Smarandache's work [7] in algebra, analysis, matrix computing, and geometry [1][2][3][4][5][6][8][9][10][11][12][13][14][15].…”