{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7IXUHRG6X43JJINQMVU5SVF22F","short_pith_number":"pith:7IXUHRG6","canonical_record":{"source":{"id":"1404.3793","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-04-15T01:13:39Z","cross_cats_sorted":[],"title_canon_sha256":"56adbec96bbaa58a23dd4c75d90caf5185710d728c3c92860129fe42567690b5","abstract_canon_sha256":"28922f0ce2f378399245789d8b6c634f3c937027664d8892af21f5899bc63580"},"schema_version":"1.0"},"canonical_sha256":"fa2f43c4debf3694a1b06569d954bad17f950bc94e72b6f0d3bcdbd97f9b390a","source":{"kind":"arxiv","id":"1404.3793","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.3793","created_at":"2026-05-18T02:54:13Z"},{"alias_kind":"arxiv_version","alias_value":"1404.3793v1","created_at":"2026-05-18T02:54:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.3793","created_at":"2026-05-18T02:54:13Z"},{"alias_kind":"pith_short_12","alias_value":"7IXUHRG6X43J","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7IXUHRG6X43JJINQ","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7IXUHRG6","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7IXUHRG6X43JJINQMVU5SVF22F","target":"record","payload":{"canonical_record":{"source":{"id":"1404.3793","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-04-15T01:13:39Z","cross_cats_sorted":[],"title_canon_sha256":"56adbec96bbaa58a23dd4c75d90caf5185710d728c3c92860129fe42567690b5","abstract_canon_sha256":"28922f0ce2f378399245789d8b6c634f3c937027664d8892af21f5899bc63580"},"schema_version":"1.0"},"canonical_sha256":"fa2f43c4debf3694a1b06569d954bad17f950bc94e72b6f0d3bcdbd97f9b390a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:13.597600Z","signature_b64":"RkC7+LP7X2wnx0twNy9qYDtbV9sL6XgELbpr/jSyXJzkFjtCYwXpoJELyNWm63XM0Gm6MX06ppQLSSA1FlvTCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa2f43c4debf3694a1b06569d954bad17f950bc94e72b6f0d3bcdbd97f9b390a","last_reissued_at":"2026-05-18T02:54:13.597118Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:13.597118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.3793","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:54:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LrZtwjnuEMQBZG2tUJp4wwUc4DXAU4a+Gc76pnTa8Vd8/bTht3YwF3s/KBUjCp9we2b3/NkYKfihlkCXujMNDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:03:55.174482Z"},"content_sha256":"60306752456df849a3d3d796a2bd1c1b8aca187380a8d54f38869ca771540fc3","schema_version":"1.0","event_id":"sha256:60306752456df849a3d3d796a2bd1c1b8aca187380a8d54f38869ca771540fc3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7IXUHRG6X43JJINQMVU5SVF22F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pr\\^ufer property in amalgamated algebras along an ideal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Moutu Abdou Salam Moutui, Najib Mahdou","submitted_at":"2014-04-15T01:13:39Z","abstract_excerpt":"Let $f : A \\rightarrow B$ be a ring homomorphism and $J$ be an ideal of $B$. In this paper, we give a characterization of zero divisors of the amalgamation which is a generalization of Maimani's and Yassemi's work (see \\cite{y}). Also, we investigate the transfer of Pr\\\"ufer domain concept to commutative rings with zero divisors in the amalgamation of $A$ with $B$ along $J$ with respect to $f$ (denoted by $A\\bowtie^fJ),$ introduced and studied by D'Anna, Finocchiaro and Fontana in 2009 (see \\cite{AFF1} and \\cite{AFF2}). Our aim is to provide new classes of commutative rings satisfying this pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3793","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:54:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cK6C3EaEApSMjvp3aQKIki5sQRMxKv8BWbhyeugBNickVLg+nhy9a6Vhr+e/AyL8Og2fkSRfoXjE9LZjB/GnBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:03:55.174833Z"},"content_sha256":"f4ac8f1f487b8e462c697c5df47892fbfafcf6e5fa62e87aa2416d5618b68951","schema_version":"1.0","event_id":"sha256:f4ac8f1f487b8e462c697c5df47892fbfafcf6e5fa62e87aa2416d5618b68951"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7IXUHRG6X43JJINQMVU5SVF22F/bundle.json","state_url":"https://pith.science/pith/7IXUHRG6X43JJINQMVU5SVF22F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7IXUHRG6X43JJINQMVU5SVF22F/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T21:03:55Z","links":{"resolver":"https://pith.science/pith/7IXUHRG6X43JJINQMVU5SVF22F","bundle":"https://pith.science/pith/7IXUHRG6X43JJINQMVU5SVF22F/bundle.json","state":"https://pith.science/pith/7IXUHRG6X43JJINQMVU5SVF22F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7IXUHRG6X43JJINQMVU5SVF22F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7IXUHRG6X43JJINQMVU5SVF22F","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":"28922f0ce2f378399245789d8b6c634f3c937027664d8892af21f5899bc63580","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-04-15T01:13:39Z","title_canon_sha256":"56adbec96bbaa58a23dd4c75d90caf5185710d728c3c92860129fe42567690b5"},"schema_version":"1.0","source":{"id":"1404.3793","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.3793","created_at":"2026-05-18T02:54:13Z"},{"alias_kind":"arxiv_version","alias_value":"1404.3793v1","created_at":"2026-05-18T02:54:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.3793","created_at":"2026-05-18T02:54:13Z"},{"alias_kind":"pith_short_12","alias_value":"7IXUHRG6X43J","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7IXUHRG6X43JJINQ","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7IXUHRG6","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:f4ac8f1f487b8e462c697c5df47892fbfafcf6e5fa62e87aa2416d5618b68951","target":"graph","created_at":"2026-05-18T02:54:13Z","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":"Let $f : A \\rightarrow B$ be a ring homomorphism and $J$ be an ideal of $B$. In this paper, we give a characterization of zero divisors of the amalgamation which is a generalization of Maimani's and Yassemi's work (see \\cite{y}). Also, we investigate the transfer of Pr\\\"ufer domain concept to commutative rings with zero divisors in the amalgamation of $A$ with $B$ along $J$ with respect to $f$ (denoted by $A\\bowtie^fJ),$ introduced and studied by D'Anna, Finocchiaro and Fontana in 2009 (see \\cite{AFF1} and \\cite{AFF2}). Our aim is to provide new classes of commutative rings satisfying this pro","authors_text":"Moutu Abdou Salam Moutui, Najib Mahdou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-04-15T01:13:39Z","title":"Pr\\^ufer property in amalgamated algebras along an ideal"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3793","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":"sha256:60306752456df849a3d3d796a2bd1c1b8aca187380a8d54f38869ca771540fc3","target":"record","created_at":"2026-05-18T02:54:13Z","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":"28922f0ce2f378399245789d8b6c634f3c937027664d8892af21f5899bc63580","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-04-15T01:13:39Z","title_canon_sha256":"56adbec96bbaa58a23dd4c75d90caf5185710d728c3c92860129fe42567690b5"},"schema_version":"1.0","source":{"id":"1404.3793","kind":"arxiv","version":1}},"canonical_sha256":"fa2f43c4debf3694a1b06569d954bad17f950bc94e72b6f0d3bcdbd97f9b390a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa2f43c4debf3694a1b06569d954bad17f950bc94e72b6f0d3bcdbd97f9b390a","first_computed_at":"2026-05-18T02:54:13.597118Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:13.597118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RkC7+LP7X2wnx0twNy9qYDtbV9sL6XgELbpr/jSyXJzkFjtCYwXpoJELyNWm63XM0Gm6MX06ppQLSSA1FlvTCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:13.597600Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.3793","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60306752456df849a3d3d796a2bd1c1b8aca187380a8d54f38869ca771540fc3","sha256:f4ac8f1f487b8e462c697c5df47892fbfafcf6e5fa62e87aa2416d5618b68951"],"state_sha256":"08b1bc9c4ac6eae59477a916017698b7fee3d10729fc65eb9af2ba491aa1d369"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ufcaNEf2fVlZ/4jDTSH3JJg5Xdxn7iaZnHfH44xdFnQ0j/N/fqD2TE8DoVER1Cud7STNWRI+KFdTBJ3/5WqcAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T21:03:55.176868Z","bundle_sha256":"6acf9e2cae09c16c97904aa5b523d6f44f5a3a3d4aa54ae9fd532f76a8e2d538"}}