Document Type : Research Paper

**Authors**

Department of Mathematics, Jundi-Shapur University of Technology Dezful, Iran

10.22108/toc.2024.138005.2081

**Abstract**

Let $R$ be a commutative ring with identity, and $ \mathrm{A}(R) $ be the set of ideals with non-zero annihilator. The annihilating-ideal graph of $ R $ is defined as the graph $AG(R)$ with the vertex set $ \mathrm{A}(R)^{*}=\mathrm{A}(R)\setminus\lbrace 0\rbrace $ and two distinct vertices $ I $ and $ J $ are adjacent if and only if $ IJ=0 $. In this paper, we characterize all positive integers $n$ for which $AG(\mathbb{Z}_n)$ is identifiable.

**Keywords**

**Main Subjects**

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Articles in Press, Corrected Proof

Available Online from 21 February 2024

**Receive Date:**10 June 2023**Revise Date:**28 January 2024**Accept Date:**05 February 2024**Published Online:**21 February 2024