{"paper":{"title":"Cohomological dimension filtration and annihilators of top local cohomology modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ali Atazadeh, Monireh Sedghi, Reza Naghipour","submitted_at":"2013-12-04T17:14:30Z","abstract_excerpt":"Let $\\frak a$ denote an ideal in a commutative Noetherian ring $R$ and $M$ a finitely generated $R$-module. In this paper, we introduce the concept of the cohomological dimension filtration $\\mathscr{M} =\\{M_i\\}_{i=0}^c$, where $ c={\\rm cd} ({\\frak a},M)$ and $M_i$ denotes the largest submodule of $M$ such that ${\\rm cd} ({\\frak a}, M_i)\\leq i.$ Some properties of this filtration are investigated. In particular, in the case that $(R, \\frak m)$ is local and $c= \\dim M$, we are able to determine the annihilator of the top local cohomology module $H_{\\frak a}^c(M)$. In fact, it is shown that ${\\r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1330","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"}