{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:AY2LSM7RPRLSMK76IZWW3BGKDQ","short_pith_number":"pith:AY2LSM7R","schema_version":"1.0","canonical_sha256":"0634b933f17c57262bfe466d6d84ca1c28900737e00490eb18c5d64db019073b","source":{"kind":"arxiv","id":"1808.01809","version":4},"attestation_state":"computed","paper":{"title":"Gorenstein-projective and semi-Gorenstein-projective modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Claus Michael Ringel, Pu Zhang","submitted_at":"2018-08-06T10:13:55Z","abstract_excerpt":"An A-module M will be said to be semi-Gorenstein-projective provided that Ext^i(M,A) = 0 for all i > 0. All Gorenstein-projective modules are semi-Gorenstein-projective and only few and quite complicated examples of semi-Gorenstein-projective modules which are not Gorenstein-projective have been known. The aim of the paper is to provide conditions on A such that all semi-Gorenstein-projective modules are Gorenstein-projective (we call such an algebra left weakly Gorenstein). In particular, we show that in case there are only finitely many isomorphism classes of indecomposable left modules whic"},"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":"1808.01809","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-08-06T10:13:55Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"0914f6aa4ed07e5c88dc62b114f15bb43689e08621baff74657edda9a8acc597","abstract_canon_sha256":"f0165de3dc4020b47a22656e343c50d5c77970015ae14bf124a5d91623d7e21b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:48:36.147052Z","signature_b64":"wGIXqm5lxsjK4oViD5RbfiWEq7jQYMIIejmDkko3iNGuS2npKE6KhWlyndpZYcgVPS3Q5ipVcTb2Mw+RCcPeCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0634b933f17c57262bfe466d6d84ca1c28900737e00490eb18c5d64db019073b","last_reissued_at":"2026-07-05T00:48:36.146689Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:48:36.146689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gorenstein-projective and semi-Gorenstein-projective modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Claus Michael Ringel, Pu Zhang","submitted_at":"2018-08-06T10:13:55Z","abstract_excerpt":"An A-module M will be said to be semi-Gorenstein-projective provided that Ext^i(M,A) = 0 for all i > 0. All Gorenstein-projective modules are semi-Gorenstein-projective and only few and quite complicated examples of semi-Gorenstein-projective modules which are not Gorenstein-projective have been known. The aim of the paper is to provide conditions on A such that all semi-Gorenstein-projective modules are Gorenstein-projective (we call such an algebra left weakly Gorenstein). In particular, we show that in case there are only finitely many isomorphism classes of indecomposable left modules whic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01809","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1808.01809/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1808.01809","created_at":"2026-07-05T00:48:36.146739+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.01809v4","created_at":"2026-07-05T00:48:36.146739+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01809","created_at":"2026-07-05T00:48:36.146739+00:00"},{"alias_kind":"pith_short_12","alias_value":"AY2LSM7RPRLS","created_at":"2026-07-05T00:48:36.146739+00:00"},{"alias_kind":"pith_short_16","alias_value":"AY2LSM7RPRLSMK76","created_at":"2026-07-05T00:48:36.146739+00:00"},{"alias_kind":"pith_short_8","alias_value":"AY2LSM7R","created_at":"2026-07-05T00:48:36.146739+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.04738","citing_title":"On weakly Gorenstein algebras","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AY2LSM7RPRLSMK76IZWW3BGKDQ","json":"https://pith.science/pith/AY2LSM7RPRLSMK76IZWW3BGKDQ.json","graph_json":"https://pith.science/api/pith-number/AY2LSM7RPRLSMK76IZWW3BGKDQ/graph.json","events_json":"https://pith.science/api/pith-number/AY2LSM7RPRLSMK76IZWW3BGKDQ/events.json","paper":"https://pith.science/paper/AY2LSM7R"},"agent_actions":{"view_html":"https://pith.science/pith/AY2LSM7RPRLSMK76IZWW3BGKDQ","download_json":"https://pith.science/pith/AY2LSM7RPRLSMK76IZWW3BGKDQ.json","view_paper":"https://pith.science/paper/AY2LSM7R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.01809&json=true","fetch_graph":"https://pith.science/api/pith-number/AY2LSM7RPRLSMK76IZWW3BGKDQ/graph.json","fetch_events":"https://pith.science/api/pith-number/AY2LSM7RPRLSMK76IZWW3BGKDQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AY2LSM7RPRLSMK76IZWW3BGKDQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AY2LSM7RPRLSMK76IZWW3BGKDQ/action/storage_attestation","attest_author":"https://pith.science/pith/AY2LSM7RPRLSMK76IZWW3BGKDQ/action/author_attestation","sign_citation":"https://pith.science/pith/AY2LSM7RPRLSMK76IZWW3BGKDQ/action/citation_signature","submit_replication":"https://pith.science/pith/AY2LSM7RPRLSMK76IZWW3BGKDQ/action/replication_record"}},"created_at":"2026-07-05T00:48:36.146739+00:00","updated_at":"2026-07-05T00:48:36.146739+00:00"}