In The Graph Based on a Given Ideal of a Ring

Abstract

In this paper we introduce a new kind of graph associated with a commutative ring with identity, and we discover some of its characterizations and properties. Let R be a commutative ring with identity and K be a non-trivial ideal of R. The graph-based on an ideal K, denoted by (R), is the undirected graph whose vertices are non-trivial ideals of R and two of its vertices are adjacent if and only if IJ⊂K.

Keywords

• Graphs
• Annihilating-Ideal Graphs
• Zero Divisor Graphs
• Graphs based on the ideals.