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As a consequence we deduce that $f_I(R)={\\rm max}\\{1, {\\rm ht}\\ I\\}$ and if ${\\frak m}\\mathrm{Ass}_R(R/I)$ is cotained in Ass$_R(R)$, then the ring $R/ I+\\cup_{n\\geq 1}(0:_RI^n)$ is equidimensional of dimension $\\dim R-1$. Moreover, we will obtain a lower bound for injective dimension of the local cohomology module $H^{{\\rm ht}\\ I}_I(R)$, in the case $(R, \\fr"},"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":"1703.00741","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-03-02T11:56:34Z","cross_cats_sorted":[],"title_canon_sha256":"169809069060c2ab00b6dde7327f0d4e1087a25f1ac5a49e6de9ee054cbac727","abstract_canon_sha256":"649f13f57d653de9bb70a32f6fb5f8acc6cefefdef161ca9cd34af866141f27c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:40.917201Z","signature_b64":"2oIAe2VWaRmyeLtZn+pYjD3YRCiPfE0ukN7vJIH9KAD1XcH3hH3gJgjGBsucxIRELzMq3cZTenSAY8YcU/RECQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b25e56f39ca33ba72a3fe6f9f40228bcad2cd1ad1a4c011f8a34b9ab0c75b880","last_reissued_at":"2026-05-18T00:49:40.916703Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:40.916703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Faltings' finiteness dimension of local cohomology modules over local Cohen-Macaulay rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Kamal Bahmanpour, Reza Naghipour","submitted_at":"2017-03-02T11:56:34Z","abstract_excerpt":"Let $(R, \\frak m)$ denote a local Cohen-Macaulay ring and $I$ a non-nilpotent ideal of $R$. The purpose of this article is to investigate Faltings' finiteness dimension $f_I(R)$ and equidimensionalness of certain homomorphic image of $R$. As a consequence we deduce that $f_I(R)={\\rm max}\\{1, {\\rm ht}\\ I\\}$ and if ${\\frak m}\\mathrm{Ass}_R(R/I)$ is cotained in Ass$_R(R)$, then the ring $R/ I+\\cup_{n\\geq 1}(0:_RI^n)$ is equidimensional of dimension $\\dim R-1$. Moreover, we will obtain a lower bound for injective dimension of the local cohomology module $H^{{\\rm ht}\\ I}_I(R)$, in the case $(R, \\fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00741","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":"1703.00741","created_at":"2026-05-18T00:49:40.916779+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.00741v1","created_at":"2026-05-18T00:49:40.916779+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00741","created_at":"2026-05-18T00:49:40.916779+00:00"},{"alias_kind":"pith_short_12","alias_value":"WJPFN444UM52","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"WJPFN444UM52OKR7","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"WJPFN444","created_at":"2026-05-18T12:31:53.515858+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/WJPFN444UM52OKR74347IARIXS","json":"https://pith.science/pith/WJPFN444UM52OKR74347IARIXS.json","graph_json":"https://pith.science/api/pith-number/WJPFN444UM52OKR74347IARIXS/graph.json","events_json":"https://pith.science/api/pith-number/WJPFN444UM52OKR74347IARIXS/events.json","paper":"https://pith.science/paper/WJPFN444"},"agent_actions":{"view_html":"https://pith.science/pith/WJPFN444UM52OKR74347IARIXS","download_json":"https://pith.science/pith/WJPFN444UM52OKR74347IARIXS.json","view_paper":"https://pith.science/paper/WJPFN444","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.00741&json=true","fetch_graph":"https://pith.science/api/pith-number/WJPFN444UM52OKR74347IARIXS/graph.json","fetch_events":"https://pith.science/api/pith-number/WJPFN444UM52OKR74347IARIXS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WJPFN444UM52OKR74347IARIXS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WJPFN444UM52OKR74347IARIXS/action/storage_attestation","attest_author":"https://pith.science/pith/WJPFN444UM52OKR74347IARIXS/action/author_attestation","sign_citation":"https://pith.science/pith/WJPFN444UM52OKR74347IARIXS/action/citation_signature","submit_replication":"https://pith.science/pith/WJPFN444UM52OKR74347IARIXS/action/replication_record"}},"created_at":"2026-05-18T00:49:40.916779+00:00","updated_at":"2026-05-18T00:49:40.916779+00:00"}