{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:PSYGIWFKBRBUFRFSKLTJ6KJWPZ","short_pith_number":"pith:PSYGIWFK","schema_version":"1.0","canonical_sha256":"7cb06458aa0c4342c4b252e69f29367e70bc99dfa4cec902f10170afeca2315b","source":{"kind":"arxiv","id":"1309.0431","version":1},"attestation_state":"computed","paper":{"title":"On the finiteness of Bass numbers of local cohomology modules and Cominimaxness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Kamal Bahmanpour, Monireh Sedghi, Reza Naghipour","submitted_at":"2013-09-02T15:03:41Z","abstract_excerpt":"In this paper, we continue the study of cominimaxness modules with respect to an ideal of a commutative Noetherian ring (cf. \\cite{ANV}), and\n  Bass numbers of local cohomology modules.\n  Let $R$ denote a commutative Noetherian local ring and $I$ an ideal of $R$. We first show that the Bass numbers $\\mu^0(\\frak p, H^2_I(R))$ and $\\mu^1(\\frak p, H^2_I(R))$ are finite for all $\\frak p\\in \\Spec R$, whenever $R$ is regular. As a consequence, it follows that the Goldie dimension of $H^2_I(R)$ is finite. Also, for a finitely generated $R$-module $M$ of dimension $d$, it is shown that the Bass number"},"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":"1309.0431","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-09-02T15:03:41Z","cross_cats_sorted":[],"title_canon_sha256":"b6a59b1204f1bf61809a6864194edc21718222b237f038e5c0fcd490ecf2050b","abstract_canon_sha256":"0455a19f14142bde70eaf38bd76124920699734157f8ca8e2f691bd99073edf0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:27.321277Z","signature_b64":"iZ54iKqt3s4yacq2ip9Sidlk5AKXsKCKiLGwBuggXvJELDXMy9eplJLObP19sYzMbeUUoyhvhoaPeAzz+UuMAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7cb06458aa0c4342c4b252e69f29367e70bc99dfa4cec902f10170afeca2315b","last_reissued_at":"2026-05-18T03:14:27.320880Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:27.320880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the finiteness of Bass numbers of local cohomology modules and Cominimaxness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Kamal Bahmanpour, Monireh Sedghi, Reza Naghipour","submitted_at":"2013-09-02T15:03:41Z","abstract_excerpt":"In this paper, we continue the study of cominimaxness modules with respect to an ideal of a commutative Noetherian ring (cf. \\cite{ANV}), and\n  Bass numbers of local cohomology modules.\n  Let $R$ denote a commutative Noetherian local ring and $I$ an ideal of $R$. We first show that the Bass numbers $\\mu^0(\\frak p, H^2_I(R))$ and $\\mu^1(\\frak p, H^2_I(R))$ are finite for all $\\frak p\\in \\Spec R$, whenever $R$ is regular. As a consequence, it follows that the Goldie dimension of $H^2_I(R)$ is finite. Also, for a finitely generated $R$-module $M$ of dimension $d$, it is shown that the Bass number"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0431","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":"1309.0431","created_at":"2026-05-18T03:14:27.320941+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.0431v1","created_at":"2026-05-18T03:14:27.320941+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0431","created_at":"2026-05-18T03:14:27.320941+00:00"},{"alias_kind":"pith_short_12","alias_value":"PSYGIWFKBRBU","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"PSYGIWFKBRBUFRFS","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"PSYGIWFK","created_at":"2026-05-18T12:27:57.521954+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/PSYGIWFKBRBUFRFSKLTJ6KJWPZ","json":"https://pith.science/pith/PSYGIWFKBRBUFRFSKLTJ6KJWPZ.json","graph_json":"https://pith.science/api/pith-number/PSYGIWFKBRBUFRFSKLTJ6KJWPZ/graph.json","events_json":"https://pith.science/api/pith-number/PSYGIWFKBRBUFRFSKLTJ6KJWPZ/events.json","paper":"https://pith.science/paper/PSYGIWFK"},"agent_actions":{"view_html":"https://pith.science/pith/PSYGIWFKBRBUFRFSKLTJ6KJWPZ","download_json":"https://pith.science/pith/PSYGIWFKBRBUFRFSKLTJ6KJWPZ.json","view_paper":"https://pith.science/paper/PSYGIWFK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.0431&json=true","fetch_graph":"https://pith.science/api/pith-number/PSYGIWFKBRBUFRFSKLTJ6KJWPZ/graph.json","fetch_events":"https://pith.science/api/pith-number/PSYGIWFKBRBUFRFSKLTJ6KJWPZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PSYGIWFKBRBUFRFSKLTJ6KJWPZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PSYGIWFKBRBUFRFSKLTJ6KJWPZ/action/storage_attestation","attest_author":"https://pith.science/pith/PSYGIWFKBRBUFRFSKLTJ6KJWPZ/action/author_attestation","sign_citation":"https://pith.science/pith/PSYGIWFKBRBUFRFSKLTJ6KJWPZ/action/citation_signature","submit_replication":"https://pith.science/pith/PSYGIWFKBRBUFRFSKLTJ6KJWPZ/action/replication_record"}},"created_at":"2026-05-18T03:14:27.320941+00:00","updated_at":"2026-05-18T03:14:27.320941+00:00"}