{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:CDRADXBVZDG5LV52RHLQJA6NSK","short_pith_number":"pith:CDRADXBV","schema_version":"1.0","canonical_sha256":"10e201dc35c8cdd5d7ba89d70483cd92a2f8654a88c920cd1037c15494482319","source":{"kind":"arxiv","id":"1903.01315","version":1},"attestation_state":"computed","paper":{"title":"On the index of reducibility of parameter ideals: The stable and limit values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Nguyen Tu Cuong, Pham Hung Quy","submitted_at":"2019-03-04T15:48:23Z","abstract_excerpt":"Let $(R, \\frak m)$ be a Noetherian local ring and $M$ a finitely generated $R$-module of dimension $d$. A famous result of Northcott says that if $M$ is Cohen-Macaulay, then the index of reducibility of parameter ideals on $M$ is an invariant of the module. The aim of this paper is to extend Northcott's theorem for any finitely generated $R$-module. We call this invariant the stable value of the indices of reducibility of parameter ideals of $M$. We also introduce the limit value of the indices of reducibility of parameter ideals of $M$."},"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":"1903.01315","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-04T15:48:23Z","cross_cats_sorted":[],"title_canon_sha256":"2138fa658904abef782e9bf139e9149361a50d8f0e9484f761233d17dae718b2","abstract_canon_sha256":"7e2bae72f6a748ec22567a5dbb348b9c27ecbbe0fc806e88a1eb0eb2348107ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:09.107980Z","signature_b64":"HTT0pnz86nNoCIzs6ExduX5QfbTiD1Ugtgt6YFej81meTFPFQ4CK1+UqSiGqiYG1XuPm30MJq3WkzFTI7otoBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10e201dc35c8cdd5d7ba89d70483cd92a2f8654a88c920cd1037c15494482319","last_reissued_at":"2026-05-17T23:52:09.106946Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:09.106946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the index of reducibility of parameter ideals: The stable and limit values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Nguyen Tu Cuong, Pham Hung Quy","submitted_at":"2019-03-04T15:48:23Z","abstract_excerpt":"Let $(R, \\frak m)$ be a Noetherian local ring and $M$ a finitely generated $R$-module of dimension $d$. A famous result of Northcott says that if $M$ is Cohen-Macaulay, then the index of reducibility of parameter ideals on $M$ is an invariant of the module. The aim of this paper is to extend Northcott's theorem for any finitely generated $R$-module. We call this invariant the stable value of the indices of reducibility of parameter ideals of $M$. We also introduce the limit value of the indices of reducibility of parameter ideals of $M$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01315","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":"1903.01315","created_at":"2026-05-17T23:52:09.107288+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.01315v1","created_at":"2026-05-17T23:52:09.107288+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.01315","created_at":"2026-05-17T23:52:09.107288+00:00"},{"alias_kind":"pith_short_12","alias_value":"CDRADXBVZDG5","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"CDRADXBVZDG5LV52","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"CDRADXBV","created_at":"2026-05-18T12:33:12.712433+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/CDRADXBVZDG5LV52RHLQJA6NSK","json":"https://pith.science/pith/CDRADXBVZDG5LV52RHLQJA6NSK.json","graph_json":"https://pith.science/api/pith-number/CDRADXBVZDG5LV52RHLQJA6NSK/graph.json","events_json":"https://pith.science/api/pith-number/CDRADXBVZDG5LV52RHLQJA6NSK/events.json","paper":"https://pith.science/paper/CDRADXBV"},"agent_actions":{"view_html":"https://pith.science/pith/CDRADXBVZDG5LV52RHLQJA6NSK","download_json":"https://pith.science/pith/CDRADXBVZDG5LV52RHLQJA6NSK.json","view_paper":"https://pith.science/paper/CDRADXBV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.01315&json=true","fetch_graph":"https://pith.science/api/pith-number/CDRADXBVZDG5LV52RHLQJA6NSK/graph.json","fetch_events":"https://pith.science/api/pith-number/CDRADXBVZDG5LV52RHLQJA6NSK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CDRADXBVZDG5LV52RHLQJA6NSK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CDRADXBVZDG5LV52RHLQJA6NSK/action/storage_attestation","attest_author":"https://pith.science/pith/CDRADXBVZDG5LV52RHLQJA6NSK/action/author_attestation","sign_citation":"https://pith.science/pith/CDRADXBVZDG5LV52RHLQJA6NSK/action/citation_signature","submit_replication":"https://pith.science/pith/CDRADXBVZDG5LV52RHLQJA6NSK/action/replication_record"}},"created_at":"2026-05-17T23:52:09.107288+00:00","updated_at":"2026-05-17T23:52:09.107288+00:00"}