The Graph of Annihilating Ideals

Abstract

Let R be a commutative ring with identity and AG(R) be the set of ideals with non-zero annihilators. The annihilating ideal graph AG(R) is a graph of vertex set AG (R){(0)} and two distinct ideal vertices I and J are adjacent if and only if . In this paper , we establish a new fundamental properties of AG(R) as well as its connection with Γ(R).

Keywords

• annihilating ideal graph
• zero divisor graph
• reduced rings
• finite local rings
• rings integer modulo n