{"paper":{"title":"Some results on the annihilators and attached primes of 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":"2017-07-19T16:56:26Z","abstract_excerpt":"Let $(R, \\frak m)$ be a local ring and $M$ a finitely generated $R$-module. It is shown that if $M$ is relative Cohen-Macaulay with respect to an ideal $\\frak a$ of $R$, then $\\text{Ann}_R(H_{\\mathfrak{a}}^{\\text{cd}(\\mathfrak{a}, M)}(M))=\\text{Ann}_RM/L=\\text{Ann}_RM$ and $\\text{Ass}_R(R/\\text{Ann}_RM)\\subseteq \\{\\mathfrak{p} \\in \\text{Ass}_R M|\\,{\\rm cd}(\\mathfrak{a}, R/\\mathfrak{p})=\\text{cd}(\\mathfrak{a}, M)\\},$ where $L$ is the largest submodule of $M$ such that ${\\rm cd}(\\mathfrak{a}, L)< {\\rm cd}(\\mathfrak{a}, M)$. We also show that if $H^{\\dim M}_{\\mathfrak{a}}(M)=0$, then $\\text{Att}_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06536","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"}