{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ZITUGW25MQD46GVA7TJO3Y5OWM","short_pith_number":"pith:ZITUGW25","schema_version":"1.0","canonical_sha256":"ca27435b5d6407cf1aa0fcd2ede3aeb31451445a1ec63736f4136c666de2b0ac","source":{"kind":"arxiv","id":"1702.05902","version":3},"attestation_state":"computed","paper":{"title":"Excellent extensions and homological conjectures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Yingying Zhang","submitted_at":"2017-02-20T09:01:20Z","abstract_excerpt":"In this paper, we introduce the notion of excellent extension of rings. Let $\\Gamma$ be an excellent extension of an artin algebra $\\Lambda$, we prove that $\\Lambda$ satisfies the Gorenstein symmetry conjecture (resp. finitistic dimension conjecture, Auslander-Gorenstein conjecture, Nakayama conjecture) if and only if so does $\\Gamma$. As a special case of excellent extensions, if $G$ is a finite group whose order is invertible in $\\Lambda$ acting on $\\Lambda$ and $\\Lambda$ is $G$-stable, we prove that if the skew group algebras $\\Lambda G$ satisfies strong Nakayama conjecture (resp. generaliz"},"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":"1702.05902","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-02-20T09:01:20Z","cross_cats_sorted":[],"title_canon_sha256":"b0bb07819c12eae62180bb3620e870e721d229b4b6655d5db8de17061eb074af","abstract_canon_sha256":"0342353d5aac5adb493815e861c43a4d05e35708efed0d6515b3ac234a61bf9d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:09.659203Z","signature_b64":"9H7Z4sGDzclv60nrZopbXcVjgjy1YpmPImS4zxtB6bxdkrjRL9epGuTzN/i6MoPn5DzW60wJlYKPrUdWl1bWAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca27435b5d6407cf1aa0fcd2ede3aeb31451445a1ec63736f4136c666de2b0ac","last_reissued_at":"2026-05-18T00:27:09.658531Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:09.658531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Excellent extensions and homological conjectures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Yingying Zhang","submitted_at":"2017-02-20T09:01:20Z","abstract_excerpt":"In this paper, we introduce the notion of excellent extension of rings. Let $\\Gamma$ be an excellent extension of an artin algebra $\\Lambda$, we prove that $\\Lambda$ satisfies the Gorenstein symmetry conjecture (resp. finitistic dimension conjecture, Auslander-Gorenstein conjecture, Nakayama conjecture) if and only if so does $\\Gamma$. As a special case of excellent extensions, if $G$ is a finite group whose order is invertible in $\\Lambda$ acting on $\\Lambda$ and $\\Lambda$ is $G$-stable, we prove that if the skew group algebras $\\Lambda G$ satisfies strong Nakayama conjecture (resp. generaliz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05902","kind":"arxiv","version":3},"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":"1702.05902","created_at":"2026-05-18T00:27:09.658629+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.05902v3","created_at":"2026-05-18T00:27:09.658629+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05902","created_at":"2026-05-18T00:27:09.658629+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZITUGW25MQD4","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZITUGW25MQD46GVA","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZITUGW25","created_at":"2026-05-18T12:31:59.375834+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/ZITUGW25MQD46GVA7TJO3Y5OWM","json":"https://pith.science/pith/ZITUGW25MQD46GVA7TJO3Y5OWM.json","graph_json":"https://pith.science/api/pith-number/ZITUGW25MQD46GVA7TJO3Y5OWM/graph.json","events_json":"https://pith.science/api/pith-number/ZITUGW25MQD46GVA7TJO3Y5OWM/events.json","paper":"https://pith.science/paper/ZITUGW25"},"agent_actions":{"view_html":"https://pith.science/pith/ZITUGW25MQD46GVA7TJO3Y5OWM","download_json":"https://pith.science/pith/ZITUGW25MQD46GVA7TJO3Y5OWM.json","view_paper":"https://pith.science/paper/ZITUGW25","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.05902&json=true","fetch_graph":"https://pith.science/api/pith-number/ZITUGW25MQD46GVA7TJO3Y5OWM/graph.json","fetch_events":"https://pith.science/api/pith-number/ZITUGW25MQD46GVA7TJO3Y5OWM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZITUGW25MQD46GVA7TJO3Y5OWM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZITUGW25MQD46GVA7TJO3Y5OWM/action/storage_attestation","attest_author":"https://pith.science/pith/ZITUGW25MQD46GVA7TJO3Y5OWM/action/author_attestation","sign_citation":"https://pith.science/pith/ZITUGW25MQD46GVA7TJO3Y5OWM/action/citation_signature","submit_replication":"https://pith.science/pith/ZITUGW25MQD46GVA7TJO3Y5OWM/action/replication_record"}},"created_at":"2026-05-18T00:27:09.658629+00:00","updated_at":"2026-05-18T00:27:09.658629+00:00"}