Ring Classification of Ideal-Based Zero Divisor Graph with Vertices 9

Abstract

Let R be a finite commutative ring with a non-zero unit, and L be an ideal of R. focuses on expanding the notation of the Zero Divisor Graph to create what is known as the Ideal-Based Zero Divisor Graph. The main goal is to classify rings using the ideal-based Zero divisor graph that consists of 9 vertices and symbolizes (ГL(R)) by using the properties |V(ГL(R))|=|L|.|V((Г (R /L))|, |L|≥2.

Keywords

• Zero Divisor Graph
• Ideal-Based Zero Divisor Graph
• Direct Product
• Finite Ring
• Local Ring