{"paper":{"title":"The Annihilating-Ideal Graph of Commutative Rings II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AC","authors_text":"Mahmood Behboodi, Zahra Rakeei","submitted_at":"2008-08-23T13:42:38Z","abstract_excerpt":"In this paper we continue our study of annihilating-ideal graph of commutative rings, that was introduced in Part I (see [5]). Let $R$ be a commutative ring with ${\\Bbb{A}}(R)$ its set of ideals with nonzero annihilator and $Z(R)$ its set of zero divisors. The annihilating-ideal graph of $R$ is defined as the (undirected) graph ${\\Bbb{AG}}(R)$ that its vertices are $\\Bbb{A}(R)^* =\\Bbb{A}(R)\\hspace{-1mm}\\setminus\\{(0)\\}$ in which for every distinct vertices $I$ and $J$, $I\\hspace{-0.6mm}-\\hspace{-1.7mm}-\\hspace{-1.7mm}-\\hspace{-0.5mm}J$ is an edge if and only if $IJ=(0)$. First, we study the di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.3189","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}