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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}_"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1312.1253","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-12-04T17:28:49Z","cross_cats_sorted":[],"title_canon_sha256":"91337db1694aadc706fa6cc51022f9a81ee38915a05bd963dca3d161542c3cb8","abstract_canon_sha256":"e2107f7427423697185f8c16756a16934e4f6e3710c9456bc0f0d0a3a71917ce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:13.144261Z","signature_b64":"wwGlLU4e/RMVY28m97ftm9uDuckVyjQ7zWgJimjDdwOm4Dg/LA5q5H4SIRgw4PaL2N0kWc958TJOUbvMha7kDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67e2ea2f972869d60e8ed9546e347d640552ba761f0f3a594516d90f01593c4e","last_reissued_at":"2026-05-18T02:55:13.143670Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:13.143670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1312.1253","created_at":"2026-05-18T02:55:13.143756+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.1253v2","created_at":"2026-05-18T02:55:13.143756+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1253","created_at":"2026-05-18T02:55:13.143756+00:00"},{"alias_kind":"pith_short_12","alias_value":"M7ROUL4XFBU5","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"M7ROUL4XFBU5MDUO","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"M7ROUL4X","created_at":"2026-05-18T12:27:51.066281+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/M7ROUL4XFBU5MDUO3FKG4ND5MQ","json":"https://pith.science/pith/M7ROUL4XFBU5MDUO3FKG4ND5MQ.json","graph_json":"https://pith.science/api/pith-number/M7ROUL4XFBU5MDUO3FKG4ND5MQ/graph.json","events_json":"https://pith.science/api/pith-number/M7ROUL4XFBU5MDUO3FKG4ND5MQ/events.json","paper":"https://pith.science/paper/M7ROUL4X"},"agent_actions":{"view_html":"https://pith.science/pith/M7ROUL4XFBU5MDUO3FKG4ND5MQ","download_json":"https://pith.science/pith/M7ROUL4XFBU5MDUO3FKG4ND5MQ.json","view_paper":"https://pith.science/paper/M7ROUL4X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.1253&json=true","fetch_graph":"https://pith.science/api/pith-number/M7ROUL4XFBU5MDUO3FKG4ND5MQ/graph.json","fetch_events":"https://pith.science/api/pith-number/M7ROUL4XFBU5MDUO3FKG4ND5MQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M7ROUL4XFBU5MDUO3FKG4ND5MQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M7ROUL4XFBU5MDUO3FKG4ND5MQ/action/storage_attestation","attest_author":"https://pith.science/pith/M7ROUL4XFBU5MDUO3FKG4ND5MQ/action/author_attestation","sign_citation":"https://pith.science/pith/M7ROUL4XFBU5MDUO3FKG4ND5MQ/action/citation_signature","submit_replication":"https://pith.science/pith/M7ROUL4XFBU5MDUO3FKG4ND5MQ/action/replication_record"}},"created_at":"2026-05-18T02:55:13.143756+00:00","updated_at":"2026-05-18T02:55:13.143756+00:00"}