The Neutrosophic Regular and Most Important Properties that Bind Neutrosophic Ring Elements

Abstract

This research has broadened the definition of the neutrosophic regular in neutrosophic rings, similar to what is known in classical rings. We have studied the properties of neutrosophic regular elements and the most important properties that link them to the neutrosophic (zero divisor, idempotent, unit and nilpotent) elements in neutrosophic rings, and we reached several important results linking these elements to each other, as some of them are different from what is known in classical rings.

Keywords

• neutrosophic ring
• neutrosophic field
• neutrosophic regular
• strongly regular
• unit
• simple nilpotent
• zero divisor