{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:7URQERV37ZBFK2YOC3225MXTQU","short_pith_number":"pith:7URQERV3","schema_version":"1.0","canonical_sha256":"fd230246bbfe42556b0e16f5aeb2f38502f0bec5e9afb06e2ee717e8fd512c0c","source":{"kind":"arxiv","id":"1707.06536","version":1},"attestation_state":"computed","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}_"},"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":"1707.06536","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-07-19T16:56:26Z","cross_cats_sorted":[],"title_canon_sha256":"8b46c431cac46de856139990f48c8ada562bf8a50e7940b65e768a2d552132eb","abstract_canon_sha256":"2d1c2ac9fd82411ea5da0c2b6bcdeb642e1ba3cc8dff52c3ee6fb3756cbcb234"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:53.597422Z","signature_b64":"5sGwFoRUiW7aymrQr0oNnm7c9YldjG7ayudNzmcD5lIKeHr2e26ghCJ1ocZGtzruF3Qo3+UE5cX+LjU5g6bQDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd230246bbfe42556b0e16f5aeb2f38502f0bec5e9afb06e2ee717e8fd512c0c","last_reissued_at":"2026-05-18T00:39:53.596734Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:53.596734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.06536","created_at":"2026-05-18T00:39:53.596822+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.06536v1","created_at":"2026-05-18T00:39:53.596822+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06536","created_at":"2026-05-18T00:39:53.596822+00:00"},{"alias_kind":"pith_short_12","alias_value":"7URQERV37ZBF","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"7URQERV37ZBFK2YO","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"7URQERV3","created_at":"2026-05-18T12:31:05.417338+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/7URQERV37ZBFK2YOC3225MXTQU","json":"https://pith.science/pith/7URQERV37ZBFK2YOC3225MXTQU.json","graph_json":"https://pith.science/api/pith-number/7URQERV37ZBFK2YOC3225MXTQU/graph.json","events_json":"https://pith.science/api/pith-number/7URQERV37ZBFK2YOC3225MXTQU/events.json","paper":"https://pith.science/paper/7URQERV3"},"agent_actions":{"view_html":"https://pith.science/pith/7URQERV37ZBFK2YOC3225MXTQU","download_json":"https://pith.science/pith/7URQERV37ZBFK2YOC3225MXTQU.json","view_paper":"https://pith.science/paper/7URQERV3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.06536&json=true","fetch_graph":"https://pith.science/api/pith-number/7URQERV37ZBFK2YOC3225MXTQU/graph.json","fetch_events":"https://pith.science/api/pith-number/7URQERV37ZBFK2YOC3225MXTQU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7URQERV37ZBFK2YOC3225MXTQU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7URQERV37ZBFK2YOC3225MXTQU/action/storage_attestation","attest_author":"https://pith.science/pith/7URQERV37ZBFK2YOC3225MXTQU/action/author_attestation","sign_citation":"https://pith.science/pith/7URQERV37ZBFK2YOC3225MXTQU/action/citation_signature","submit_replication":"https://pith.science/pith/7URQERV37ZBFK2YOC3225MXTQU/action/replication_record"}},"created_at":"2026-05-18T00:39:53.596822+00:00","updated_at":"2026-05-18T00:39:53.596822+00:00"}