{"paper":{"title":"Note on linearly equivalent ideal topologies over Noetherian modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Adeleh Azari, Reza Naghipour, Simin Mollamahmoudi","submitted_at":"2016-07-26T10:43:32Z","abstract_excerpt":"Let $R$ be a commutative Noetherian ring, and let $N$ be a non-zero finitely generated $R$-module. In this paper, the main result asserts that for any $N$-proper ideal $\\frak a$ of $R,$ the $\\frak a$-symbolic topology on $N$ is linearly equivalent to the $\\frak a$-adic topology on $N$ if and only if, for every $\\frak p\\in \\Supp(N)$, $\\Ass_{R_{\\mathfrak {p} }}N_{\\mathfrak {p}}$ consists of a single prime ideal and $\\dim N\\leq 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07634","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"}