{"paper":{"title":"Modules cofinite and weakly cofinite with respect to an ideal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Kamal Bahmanpour, Monireh Sedghi, Reza Naghipour","submitted_at":"2017-03-02T12:46:26Z","abstract_excerpt":"The purpose of the present paper is to continue the study of modules cofinite and weakly cofinite with respect to an ideal $\\frak a$ of a Noetherian ring $R$. It is shown that an $R$-module $M$ is cofinite with respect to $\\frak a$, if and only if, $\\Ext^i_R(R/\\frak a,M)$ is finitely generated for all $i\\leq {\\rm cd}(\\frak a,M)+1$, whenever $\\dim R/\\frak a=1$. In addition, we show that if $M$ is finitely generated and $H^i_{\\frak a}(M)$ are weakly Laskerian for all $i\\leq t-1$, then $H^i_{\\frak a}(M)$ are ${\\frak a}$-cofinite for all $i\\leq t-1$ and for any minimax submodule $K$ of $H^{t}_{\\fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00766","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"}