The exact annihilating-ideal graph of a commutative ring

The rings considered in this article are commutative with identity. For an ideal $I$ of a ring $R$, we denote the annihilator $R$ by $Ann(I)$. An is said to be exact annihilating if there exists non-zero $J$ such that $Ann(I) = J$ and $Ann(J) I$. set all ideals $\mathbb{EA}(R)$ $\mathbb{EA}(R)\backslash \{(0)\}$ $\mathbb{EA}(R)^{*}$. Let $\mathbb{EA}(R)^{*}\neq \emptyset$. With [Exact Annihilating-ideal graph rings, {\it J. Algebra Related Topics} {\bf 5}(1) (2017) 27-33] P.T. Lalchandani introduced investigated undirected called annihilating-ideal denoted $\mathbb{EAG}(R)$ whose vertex $\mathbb{EA}(R)^{*}$ distinct vertices adjacent only In article, continue study ring. Section 2 , prove some basic properties provide several examples. 3, determine structure $\mathbb{EAG}(R)$, where either special principal or reduced which admits finite number minimal prime ideals.