{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:MUVBZMRSVPRHFHCWOZFUF6XK6U","short_pith_number":"pith:MUVBZMRS","schema_version":"1.0","canonical_sha256":"652a1cb232abe2729c56764b42faeaf533b3e29d254ccf579a3cd3b61d4c41c8","source":{"kind":"arxiv","id":"1208.5934","version":1},"attestation_state":"computed","paper":{"title":"On the local cohomology modules deffined by a pair of ideals and serre subcategories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"KH. Ahmadi-amoli, M. Y. Sadeghi","submitted_at":"2012-08-29T14:45:14Z","abstract_excerpt":"This paper is concerned about the relation between local cohomology modules defined by a pair of ideals and Serre classes of R-modules, as a generalization of results of J. Azami, R. Naghipour and B. Vakili (2009) and M. Asgharzadeh and M.Tousi (2010). Let R be a commutative Noetherian ring, I, J be two ideals of R and M be an R-module. Let a\\in \\~{W}(I; J) and t \\in N_0 be such that Ext^t_R(R/a,M)\\in S and Ext^j_R(R/a,H^i_I;J(M))\\inS for all i < t and all j>=0. Then for any submodule N of H^t_I;J(M) such that Ext^1_R(R/a;N)\\in,we obtain HomR(R=a;H^t_I;J(M)/N)\\inS."},"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":"1208.5934","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-08-29T14:45:14Z","cross_cats_sorted":[],"title_canon_sha256":"fb8f733bdb8a80b5537cc50a9cbeab40ebae607f1523854d95537101276e8cd2","abstract_canon_sha256":"0691718b148b7ff504cbdac69628b95714e3b3ee7c120ac062a83976850b1414"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:35.619719Z","signature_b64":"f239CczbMKbrb/33n1be73cnkKZaI48A1Ac9Fm+2jMviqOb3ObjZTBv9Glh5PEjWPz/EezRUJo1TE/c0bLhoBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"652a1cb232abe2729c56764b42faeaf533b3e29d254ccf579a3cd3b61d4c41c8","last_reissued_at":"2026-05-18T00:59:35.619134Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:35.619134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the local cohomology modules deffined by a pair of ideals and serre subcategories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"KH. Ahmadi-amoli, M. Y. Sadeghi","submitted_at":"2012-08-29T14:45:14Z","abstract_excerpt":"This paper is concerned about the relation between local cohomology modules defined by a pair of ideals and Serre classes of R-modules, as a generalization of results of J. Azami, R. Naghipour and B. Vakili (2009) and M. Asgharzadeh and M.Tousi (2010). Let R be a commutative Noetherian ring, I, J be two ideals of R and M be an R-module. Let a\\in \\~{W}(I; J) and t \\in N_0 be such that Ext^t_R(R/a,M)\\in S and Ext^j_R(R/a,H^i_I;J(M))\\inS for all i < t and all j>=0. Then for any submodule N of H^t_I;J(M) such that Ext^1_R(R/a;N)\\in,we obtain HomR(R=a;H^t_I;J(M)/N)\\inS."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5934","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":"1208.5934","created_at":"2026-05-18T00:59:35.619235+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.5934v1","created_at":"2026-05-18T00:59:35.619235+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5934","created_at":"2026-05-18T00:59:35.619235+00:00"},{"alias_kind":"pith_short_12","alias_value":"MUVBZMRSVPRH","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"MUVBZMRSVPRHFHCW","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"MUVBZMRS","created_at":"2026-05-18T12:27:14.488303+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/MUVBZMRSVPRHFHCWOZFUF6XK6U","json":"https://pith.science/pith/MUVBZMRSVPRHFHCWOZFUF6XK6U.json","graph_json":"https://pith.science/api/pith-number/MUVBZMRSVPRHFHCWOZFUF6XK6U/graph.json","events_json":"https://pith.science/api/pith-number/MUVBZMRSVPRHFHCWOZFUF6XK6U/events.json","paper":"https://pith.science/paper/MUVBZMRS"},"agent_actions":{"view_html":"https://pith.science/pith/MUVBZMRSVPRHFHCWOZFUF6XK6U","download_json":"https://pith.science/pith/MUVBZMRSVPRHFHCWOZFUF6XK6U.json","view_paper":"https://pith.science/paper/MUVBZMRS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.5934&json=true","fetch_graph":"https://pith.science/api/pith-number/MUVBZMRSVPRHFHCWOZFUF6XK6U/graph.json","fetch_events":"https://pith.science/api/pith-number/MUVBZMRSVPRHFHCWOZFUF6XK6U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MUVBZMRSVPRHFHCWOZFUF6XK6U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MUVBZMRSVPRHFHCWOZFUF6XK6U/action/storage_attestation","attest_author":"https://pith.science/pith/MUVBZMRSVPRHFHCWOZFUF6XK6U/action/author_attestation","sign_citation":"https://pith.science/pith/MUVBZMRSVPRHFHCWOZFUF6XK6U/action/citation_signature","submit_replication":"https://pith.science/pith/MUVBZMRSVPRHFHCWOZFUF6XK6U/action/replication_record"}},"created_at":"2026-05-18T00:59:35.619235+00:00","updated_at":"2026-05-18T00:59:35.619235+00:00"}