{"paper":{"title":"Isomorphisms between Jacobson graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AC","authors_text":"Ahmad Erfanian, Ali Azimi, Mohammad Farrokhi Derakhshandeh Ghouchan","submitted_at":"2014-01-25T20:45:15Z","abstract_excerpt":"Let $R$ be a commutative ring with a non-zero identity and $\\mathfrak{J}_R$ be its Jacobson graph. We show that if $R$ and $R'$ are finite commutative rings, then $\\mathfrak{J}_R\\cong\\mathfrak{J}_{R'}$ if and only if $|J(R)|=|J(R')|$ and $R/J(R)\\cong R'/J(R')$. Also, for a Jacobson graph $\\mathfrak{J}_R$, we obtain the structure of group $\\mathrm{Aut}(\\mathfrak{J}_R)$ of all automorphisms of $\\mathfrak{J}_R$ and prove that under some conditions two semi-simple rings $R$ and $R'$ are isomorphic if and only if $\\mathrm{Aut}(\\mathfrak{J}_R)\\cong\\mathrm{Aut}(\\mathfrak{J}_{R'})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6579","kind":"arxiv","version":1},"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"}