{"paper":{"title":"Assassins and torsion functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Fred Rohrer","submitted_at":"2017-08-29T20:23:30Z","abstract_excerpt":"Let $R$ be a ring, let $\\mathfrak{a}\\subseteq R$ be an ideal, and let $M$ be an $R$-module. Let $\\Gamma_{\\mathfrak{a}}$ denote the $\\mathfrak{a}$-torsion functor. Conditions are given for the (weakly) associated primes of $\\Gamma_{\\mathfrak{a}}(M)$ to be the (weakly) associated primes of $M$ containing $\\mathfrak{a}$, and for the (weakly) associated primes of $M/\\Gamma_{\\mathfrak{a}}(M)$ to be the (weakly) associated primes of $M$ not containing $\\mathfrak{a}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09008","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"}