{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ZWEFDVKDYVEBGW4QN66NXFK3F7","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":"22b5c3f916b1fc0f1718126d67adbc6a16521ff70b9ffe03ea4c04459e8d1536","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AC","submitted_at":"2024-09-30T19:16:33Z","title_canon_sha256":"71b7aa0427db40aba194d4c887b7ce41828f8acf5b455245b5655d651c031ef5"},"schema_version":"1.0","source":{"id":"2410.00167","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.00167","created_at":"2026-07-05T09:14:00Z"},{"alias_kind":"arxiv_version","alias_value":"2410.00167v1","created_at":"2026-07-05T09:14:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.00167","created_at":"2026-07-05T09:14:00Z"},{"alias_kind":"pith_short_12","alias_value":"ZWEFDVKDYVEB","created_at":"2026-07-05T09:14:00Z"},{"alias_kind":"pith_short_16","alias_value":"ZWEFDVKDYVEBGW4Q","created_at":"2026-07-05T09:14:00Z"},{"alias_kind":"pith_short_8","alias_value":"ZWEFDVKD","created_at":"2026-07-05T09:14:00Z"}],"graph_snapshots":[{"event_id":"sha256:482ecca702dc932e000f980dd533d3c9cfa9114ee87933dfd412cbbe25de7e61","target":"graph","created_at":"2026-07-05T09:14:00Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2410.00167/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let R be a commutative ring, and let S be a multiplicative subset of R. In this paper, we introduce and investigate the notion of S-FP-injective modules. Among other results, we show that, under certain conditions, a ring R is S-Noetherian if and only if every S-FP-injective R-module is S-injective. Moreover, we establish, under certain conditions, counterparts of Matlis, Stenstr\\\"om and Cheatham-Stone's characterizations of S-coherent rings.","authors_text":"Ayoub Bouziri, Driss Bennis","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AC","submitted_at":"2024-09-30T19:16:33Z","title":"S-FP-injective modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.00167","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":"sha256:5fc59c360c7adae804ed7ad1ee83d28d2acd3621843f2a4f5c88dd6182b41bec","target":"record","created_at":"2026-07-05T09:14:00Z","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":"22b5c3f916b1fc0f1718126d67adbc6a16521ff70b9ffe03ea4c04459e8d1536","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AC","submitted_at":"2024-09-30T19:16:33Z","title_canon_sha256":"71b7aa0427db40aba194d4c887b7ce41828f8acf5b455245b5655d651c031ef5"},"schema_version":"1.0","source":{"id":"2410.00167","kind":"arxiv","version":1}},"canonical_sha256":"cd8851d543c548135b906fbcdb955b2fc1df6b25f35bd43c3e7b435e6dc42e3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd8851d543c548135b906fbcdb955b2fc1df6b25f35bd43c3e7b435e6dc42e3d","first_computed_at":"2026-07-05T09:14:00.400341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:14:00.400341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eF1yKJaFwfNzU37p5M+wVTR2JWjLbfGCaGR8Qs/IvJCm/3b8sum9cED8RvLDKbwdL24vztgFECiaZXrsUxW9AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:14:00.400769Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.00167","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fc59c360c7adae804ed7ad1ee83d28d2acd3621843f2a4f5c88dd6182b41bec","sha256:482ecca702dc932e000f980dd533d3c9cfa9114ee87933dfd412cbbe25de7e61"],"state_sha256":"0c83e32530eee29e1f118148fc3cec8e762874676dd801a8929ee1c533a7c709"}