{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:AYQTCO7GYCXEDXD2ZT7Z43TQOD","short_pith_number":"pith:AYQTCO7G","schema_version":"1.0","canonical_sha256":"0621313be6c0ae41dc7accff9e6e7070e1e4a9c68adf885992bcec370d4d0e58","source":{"kind":"arxiv","id":"1710.09899","version":1},"attestation_state":"computed","paper":{"title":"AC-Gorenstein rings and their stable module categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"James Gillespie","submitted_at":"2017-10-26T20:10:29Z","abstract_excerpt":"We introduce what is meant by an AC-Gorenstein ring. It is a generalized notion of Gorenstein ring which is compatible with the Gorenstein AC-injective and Gorenstein AC-projective modules of Bravo-Gillespie-Hovey. It is also compatible with the notion of $n$-coherent rings introduced by Bravo-Perez: So a $0$-coherent AC-Gorenstein ring is precisely a usual Gorenstein ring in the sense of Iwanaga, while a $1$-coherent AC-Gorenstein ring is precisely a Ding-Chen ring. We show that any AC-Gorenstein ring admits a stable module category that is compactly generated and is the homotopy category of "},"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":"1710.09899","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-10-26T20:10:29Z","cross_cats_sorted":[],"title_canon_sha256":"4ec0727137b6b3f4467a2966e73c1a272c0044572c09b96bdf2140b13600ba74","abstract_canon_sha256":"f0113bc7f3d008bcb3e6cfa8121fdc6077aef38f507fa97bd8272b36a8507290"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:55.233064Z","signature_b64":"yhqXApFupXHMoKx6E5ThHLSYuuCr/YCXjpbTz6qGqxG0jDd6E3doVd25hKEjqPYhn9zGxPJNEtdFEEcyrJvmCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0621313be6c0ae41dc7accff9e6e7070e1e4a9c68adf885992bcec370d4d0e58","last_reissued_at":"2026-05-18T00:31:55.232463Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:55.232463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"AC-Gorenstein rings and their stable module categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"James Gillespie","submitted_at":"2017-10-26T20:10:29Z","abstract_excerpt":"We introduce what is meant by an AC-Gorenstein ring. It is a generalized notion of Gorenstein ring which is compatible with the Gorenstein AC-injective and Gorenstein AC-projective modules of Bravo-Gillespie-Hovey. It is also compatible with the notion of $n$-coherent rings introduced by Bravo-Perez: So a $0$-coherent AC-Gorenstein ring is precisely a usual Gorenstein ring in the sense of Iwanaga, while a $1$-coherent AC-Gorenstein ring is precisely a Ding-Chen ring. We show that any AC-Gorenstein ring admits a stable module category that is compactly generated and is the homotopy category of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09899","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":"1710.09899","created_at":"2026-05-18T00:31:55.232576+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.09899v1","created_at":"2026-05-18T00:31:55.232576+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.09899","created_at":"2026-05-18T00:31:55.232576+00:00"},{"alias_kind":"pith_short_12","alias_value":"AYQTCO7GYCXE","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"AYQTCO7GYCXEDXD2","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"AYQTCO7G","created_at":"2026-05-18T12:31:08.081275+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/AYQTCO7GYCXEDXD2ZT7Z43TQOD","json":"https://pith.science/pith/AYQTCO7GYCXEDXD2ZT7Z43TQOD.json","graph_json":"https://pith.science/api/pith-number/AYQTCO7GYCXEDXD2ZT7Z43TQOD/graph.json","events_json":"https://pith.science/api/pith-number/AYQTCO7GYCXEDXD2ZT7Z43TQOD/events.json","paper":"https://pith.science/paper/AYQTCO7G"},"agent_actions":{"view_html":"https://pith.science/pith/AYQTCO7GYCXEDXD2ZT7Z43TQOD","download_json":"https://pith.science/pith/AYQTCO7GYCXEDXD2ZT7Z43TQOD.json","view_paper":"https://pith.science/paper/AYQTCO7G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.09899&json=true","fetch_graph":"https://pith.science/api/pith-number/AYQTCO7GYCXEDXD2ZT7Z43TQOD/graph.json","fetch_events":"https://pith.science/api/pith-number/AYQTCO7GYCXEDXD2ZT7Z43TQOD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AYQTCO7GYCXEDXD2ZT7Z43TQOD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AYQTCO7GYCXEDXD2ZT7Z43TQOD/action/storage_attestation","attest_author":"https://pith.science/pith/AYQTCO7GYCXEDXD2ZT7Z43TQOD/action/author_attestation","sign_citation":"https://pith.science/pith/AYQTCO7GYCXEDXD2ZT7Z43TQOD/action/citation_signature","submit_replication":"https://pith.science/pith/AYQTCO7GYCXEDXD2ZT7Z43TQOD/action/replication_record"}},"created_at":"2026-05-18T00:31:55.232576+00:00","updated_at":"2026-05-18T00:31:55.232576+00:00"}