{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6TWFUFCA6XB7BDQWYOHUFBCBZ6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fcce76864e52b23619c4ff7588df4ef9e16cc44d77c9e286fc05b41d7b9c08d0","cross_cats_sorted":["math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-10-07T14:14:42Z","title_canon_sha256":"96ed44cd1c8482c54e1849f7f959469f00cb82f24e3824bb1b8b5e02367292fc"},"schema_version":"1.0","source":{"id":"1110.1537","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1537","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1537v1","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1537","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"pith_short_12","alias_value":"6TWFUFCA6XB7","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6TWFUFCA6XB7BDQW","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6TWFUFCA","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:452146f7c166aca35f655070b010644a4b9ec1adabe048018de84f2e90d1ae32","target":"graph","created_at":"2026-05-18T02:58:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For a ring $R$, the properties of being (left) selfinjective or being cogenerator for the left $R$-modules do not imply one another, and the two combined give rise to the important notion of PF-rings. For a coalgebra $C$, (left) self-projectivity implies that $C$ is generator for right comodules and the coalgebras with this property were called right quasi-co-Frobenius; however, whether the converse implication is true is an open question. We provide an extensive study of this problem. We show that this implication does not hold, by giving a large class of examples of coalgebras having the \"ge","authors_text":"Miodrag C Iovanov","cross_cats":["math.CT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-10-07T14:14:42Z","title":"The Generating Condition for Coalgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1537","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bdf68e48f8fe19cea0babe6530747856340288029816e06e21a233277d9c2d2b","target":"record","created_at":"2026-05-18T02:58:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fcce76864e52b23619c4ff7588df4ef9e16cc44d77c9e286fc05b41d7b9c08d0","cross_cats_sorted":["math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-10-07T14:14:42Z","title_canon_sha256":"96ed44cd1c8482c54e1849f7f959469f00cb82f24e3824bb1b8b5e02367292fc"},"schema_version":"1.0","source":{"id":"1110.1537","kind":"arxiv","version":1}},"canonical_sha256":"f4ec5a1440f5c3f08e16c38f428441cf93b0f4cd652346ff830c4a19f9703702","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4ec5a1440f5c3f08e16c38f428441cf93b0f4cd652346ff830c4a19f9703702","first_computed_at":"2026-05-18T02:58:00.363021Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:00.363021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qtuHSaSZ7GkB+cByMHr7JtkpcCVHEGrzd5/znZ/hffNf2mzcaSD3KoM75hzfeCX09BfPf65jKEkq5K8YJMPcDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:00.363669Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.1537","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bdf68e48f8fe19cea0babe6530747856340288029816e06e21a233277d9c2d2b","sha256:452146f7c166aca35f655070b010644a4b9ec1adabe048018de84f2e90d1ae32"],"state_sha256":"5043cdc45bd963316d2d4707e185e0a938635491b10074ece6b100a31361311b"}