{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:TWCXTQHYKITFK3KKMJ4TQHYKEB","short_pith_number":"pith:TWCXTQHY","schema_version":"1.0","canonical_sha256":"9d8579c0f85226556d4a6279381f0a205906df1d6070b01aa26c9d3c0590f299","source":{"kind":"arxiv","id":"1312.3804","version":3},"attestation_state":"computed","paper":{"title":"Algebraic and topological properties of an amalgamated algebra along an ideal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Carmelo Antonio Finocchiaro, Marco D'Anna, Marco Fontana","submitted_at":"2013-12-13T13:29:09Z","abstract_excerpt":"Let $f:A \\rightarrow B$ be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we study the amalgamation of $A$ with $B$ along $J$ with respect to $f$, a construction that provides a general frame for studying the amalgamated duplication of a ring along an ideal, introduced by D'Anna and Fontana in 2007, and other classical constructions (such as the $A+ XB[X]$, the $A+ XB[\\![X]\\!]$ and the $D+M$ constructions). In particular, we completely describe the prime spectrum of the amalgamation and, when it is a local Noetherian ring, we study its embedding dimension and when it turns "},"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":"1312.3804","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-12-13T13:29:09Z","cross_cats_sorted":[],"title_canon_sha256":"999087f0024ac563009ff69ca316178a0951adb72a1c614e6fbcf71b0a23932b","abstract_canon_sha256":"740ed1e14b09f85306668783542bcbedacd54df5d6830b2e05cd5a7fa039c97e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:02.021727Z","signature_b64":"2S3hJgFg9atw6xLSJT8g5EyTXpzMCenp4WR/6M65CXuN4KJlbyYU74ERb+qidfc+SwRjdcxS762r7CYl11ZjBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d8579c0f85226556d4a6279381f0a205906df1d6070b01aa26c9d3c0590f299","last_reissued_at":"2026-05-18T01:12:02.021336Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:02.021336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic and topological properties of an amalgamated algebra along an ideal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Carmelo Antonio Finocchiaro, Marco D'Anna, Marco Fontana","submitted_at":"2013-12-13T13:29:09Z","abstract_excerpt":"Let $f:A \\rightarrow B$ be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we study the amalgamation of $A$ with $B$ along $J$ with respect to $f$, a construction that provides a general frame for studying the amalgamated duplication of a ring along an ideal, introduced by D'Anna and Fontana in 2007, and other classical constructions (such as the $A+ XB[X]$, the $A+ XB[\\![X]\\!]$ and the $D+M$ constructions). In particular, we completely describe the prime spectrum of the amalgamation and, when it is a local Noetherian ring, we study its embedding dimension and when it turns "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3804","kind":"arxiv","version":3},"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":"1312.3804","created_at":"2026-05-18T01:12:02.021404+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.3804v3","created_at":"2026-05-18T01:12:02.021404+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3804","created_at":"2026-05-18T01:12:02.021404+00:00"},{"alias_kind":"pith_short_12","alias_value":"TWCXTQHYKITF","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"TWCXTQHYKITFK3KK","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"TWCXTQHY","created_at":"2026-05-18T12:28:02.375192+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/TWCXTQHYKITFK3KKMJ4TQHYKEB","json":"https://pith.science/pith/TWCXTQHYKITFK3KKMJ4TQHYKEB.json","graph_json":"https://pith.science/api/pith-number/TWCXTQHYKITFK3KKMJ4TQHYKEB/graph.json","events_json":"https://pith.science/api/pith-number/TWCXTQHYKITFK3KKMJ4TQHYKEB/events.json","paper":"https://pith.science/paper/TWCXTQHY"},"agent_actions":{"view_html":"https://pith.science/pith/TWCXTQHYKITFK3KKMJ4TQHYKEB","download_json":"https://pith.science/pith/TWCXTQHYKITFK3KKMJ4TQHYKEB.json","view_paper":"https://pith.science/paper/TWCXTQHY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.3804&json=true","fetch_graph":"https://pith.science/api/pith-number/TWCXTQHYKITFK3KKMJ4TQHYKEB/graph.json","fetch_events":"https://pith.science/api/pith-number/TWCXTQHYKITFK3KKMJ4TQHYKEB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TWCXTQHYKITFK3KKMJ4TQHYKEB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TWCXTQHYKITFK3KKMJ4TQHYKEB/action/storage_attestation","attest_author":"https://pith.science/pith/TWCXTQHYKITFK3KKMJ4TQHYKEB/action/author_attestation","sign_citation":"https://pith.science/pith/TWCXTQHYKITFK3KKMJ4TQHYKEB/action/citation_signature","submit_replication":"https://pith.science/pith/TWCXTQHYKITFK3KKMJ4TQHYKEB/action/replication_record"}},"created_at":"2026-05-18T01:12:02.021404+00:00","updated_at":"2026-05-18T01:12:02.021404+00:00"}