{"paper":{"title":"On the annihilators and attached primes 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":"2013-12-04T17:28:49Z","abstract_excerpt":"Let \\frak a be an ideal of a commutative Noetherian ring R and M a finitely generated R-module. It is shown that {\\rm Ann}_R(H_{\\frak a}^{{\\dim M}({\\frak a}, M)}(M))= {\\rm Ann}_R(M/T_R({\\frak a}, M)), where T_R({\\frak a}, M) is the largest submodule of M such that {\\rm cd}({\\frak a}, T_R({\\frak a}, M))< {\\rm cd}({\\frak a}, M). Several applications of this result are given. Among other things, it is shown that there exists an ideal \\frak b of R such that {\\rm Ann}_R(H_{\\frak a}^{\\dim M}(M))={\\rm Ann}_R(M/H_{\\frak b}^{0}(M)). Using this, we show that if H_{\\frak a}^{\\dim R}(R)=0, then {\\rm Att}_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1253","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"}