{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:T6V22XKOUBRGCGJQ32EY63BCG6","short_pith_number":"pith:T6V22XKO","schema_version":"1.0","canonical_sha256":"9fabad5d4ea062611930de898f6c22379fa6cb094cb131e1360e366083f1ed78","source":{"kind":"arxiv","id":"1308.3071","version":2},"attestation_state":"computed","paper":{"title":"Some duality and equivalence results","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Majid Rahro Zargar","submitted_at":"2013-08-14T09:34:03Z","abstract_excerpt":"Let $(R,\\fm)$ be a relative Cohen-Macaulay local ring with respect to an ideal $\\fa$ of $R$ and set $c:=\\h\\fa$. In this paper, we investigate some properties of the Matlis dual $\\H_{\\fa}^c(R)^{\\vee}$ of the $R$-module $\\H_{\\fa}^c(R)$ and we show that such modules treat like canonical modules over Cohen-Macaulay local rings. Also, we provide some duality and equivalence results with respect to the module $\\H_{\\fa}^c(R)^{\\vee}$ and so these results lead to achieve generalizations of some known results, such as the Local Duality Theorem, which have been provided over a Cohen-Macaulay local ring w"},"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":"1308.3071","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AC","submitted_at":"2013-08-14T09:34:03Z","cross_cats_sorted":[],"title_canon_sha256":"579298f55d063a64e2bede7324d3de5b2ee9673057840ce912635876312fffc6","abstract_canon_sha256":"911f9b61686ba1beb4ea6ff641ffa14a4474a7b8d40c0eaa9f40baf2a88c81fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:51.255824Z","signature_b64":"cjJT2WeprxjCFySca41VTE4iaits3Mr3/ojza19nMbeAMAnua8bT5x4v7IyL2VFDzsdACT77FULuPShZ8sRUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fabad5d4ea062611930de898f6c22379fa6cb094cb131e1360e366083f1ed78","last_reissued_at":"2026-05-18T01:34:51.255391Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:51.255391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some duality and equivalence results","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Majid Rahro Zargar","submitted_at":"2013-08-14T09:34:03Z","abstract_excerpt":"Let $(R,\\fm)$ be a relative Cohen-Macaulay local ring with respect to an ideal $\\fa$ of $R$ and set $c:=\\h\\fa$. In this paper, we investigate some properties of the Matlis dual $\\H_{\\fa}^c(R)^{\\vee}$ of the $R$-module $\\H_{\\fa}^c(R)$ and we show that such modules treat like canonical modules over Cohen-Macaulay local rings. Also, we provide some duality and equivalence results with respect to the module $\\H_{\\fa}^c(R)^{\\vee}$ and so these results lead to achieve generalizations of some known results, such as the Local Duality Theorem, which have been provided over a Cohen-Macaulay local ring w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3071","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":"1308.3071","created_at":"2026-05-18T01:34:51.255478+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.3071v2","created_at":"2026-05-18T01:34:51.255478+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3071","created_at":"2026-05-18T01:34:51.255478+00:00"},{"alias_kind":"pith_short_12","alias_value":"T6V22XKOUBRG","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"T6V22XKOUBRGCGJQ","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"T6V22XKO","created_at":"2026-05-18T12:27:59.945178+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/T6V22XKOUBRGCGJQ32EY63BCG6","json":"https://pith.science/pith/T6V22XKOUBRGCGJQ32EY63BCG6.json","graph_json":"https://pith.science/api/pith-number/T6V22XKOUBRGCGJQ32EY63BCG6/graph.json","events_json":"https://pith.science/api/pith-number/T6V22XKOUBRGCGJQ32EY63BCG6/events.json","paper":"https://pith.science/paper/T6V22XKO"},"agent_actions":{"view_html":"https://pith.science/pith/T6V22XKOUBRGCGJQ32EY63BCG6","download_json":"https://pith.science/pith/T6V22XKOUBRGCGJQ32EY63BCG6.json","view_paper":"https://pith.science/paper/T6V22XKO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.3071&json=true","fetch_graph":"https://pith.science/api/pith-number/T6V22XKOUBRGCGJQ32EY63BCG6/graph.json","fetch_events":"https://pith.science/api/pith-number/T6V22XKOUBRGCGJQ32EY63BCG6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T6V22XKOUBRGCGJQ32EY63BCG6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T6V22XKOUBRGCGJQ32EY63BCG6/action/storage_attestation","attest_author":"https://pith.science/pith/T6V22XKOUBRGCGJQ32EY63BCG6/action/author_attestation","sign_citation":"https://pith.science/pith/T6V22XKOUBRGCGJQ32EY63BCG6/action/citation_signature","submit_replication":"https://pith.science/pith/T6V22XKOUBRGCGJQ32EY63BCG6/action/replication_record"}},"created_at":"2026-05-18T01:34:51.255478+00:00","updated_at":"2026-05-18T01:34:51.255478+00:00"}