Commutative rings introduce a class of identifiable graphs
نویسندگان
1 Department of Mathematics, Jundi-Shapur University of Technology Dezful, Iran
2 Department of Mathematics, Jundi-Shapur University of Technology Dezful, Iran
3 Department of Mathematics, Jundi-Shapur University of Technology Dezful, Iran
doi
10.22108/toc.2024.138005.2081چکیده
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.
