{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:PKPNZXFEGDIMBMH7SLAB4TXQVQ","short_pith_number":"pith:PKPNZXFE","schema_version":"1.0","canonical_sha256":"7a9edcdca430d0c0b0ff92c01e4ef0ac3aa4c0287475a80e50f9a0362b167c96","source":{"kind":"arxiv","id":"1312.1663","version":1},"attestation_state":"computed","paper":{"title":"From regular modules to von Neumann regular rings via coordinatization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Leonard D\\u{a}u\\c{s}, Mohamed A. Salim","submitted_at":"2013-12-05T20:01:07Z","abstract_excerpt":"In this paper we establish a very close link (in terms of von Neumann's coordinatization) between regular modules introduced by Zelmanowitz, on one hand, and von Neumann regular rings, on the other hand: we prove that the lattice $\\mathcal{L}^{fg}(M)$ of all finitely generated submodules of a finitely generated regular module $M$, over an arbitrary ring, can be coordinatized as the lattice of all principal right ideals of some von Neumann regular ring $S$."},"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":"1312.1663","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-12-05T20:01:07Z","cross_cats_sorted":[],"title_canon_sha256":"630b6cdfb2d208a13014a79ab9a7343f49b6f54d54fd6f74a577fc203ac3e7bf","abstract_canon_sha256":"341af9829507af063d25de0e0ec7ad50186fbad9347a0361208fcad9de2268c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:26.591716Z","signature_b64":"nvSuddfYCERLRaeS3USdMRL5lpZHe3sNPoW1EkwhfL6ZWRihgDhncnosons44ZEqm/Vpr0kOdGXtWaXjmCiZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a9edcdca430d0c0b0ff92c01e4ef0ac3aa4c0287475a80e50f9a0362b167c96","last_reissued_at":"2026-05-18T03:05:26.591153Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:26.591153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From regular modules to von Neumann regular rings via coordinatization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Leonard D\\u{a}u\\c{s}, Mohamed A. Salim","submitted_at":"2013-12-05T20:01:07Z","abstract_excerpt":"In this paper we establish a very close link (in terms of von Neumann's coordinatization) between regular modules introduced by Zelmanowitz, on one hand, and von Neumann regular rings, on the other hand: we prove that the lattice $\\mathcal{L}^{fg}(M)$ of all finitely generated submodules of a finitely generated regular module $M$, over an arbitrary ring, can be coordinatized as the lattice of all principal right ideals of some von Neumann regular ring $S$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1663","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1312.1663","created_at":"2026-05-18T03:05:26.591231+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.1663v1","created_at":"2026-05-18T03:05:26.591231+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1663","created_at":"2026-05-18T03:05:26.591231+00:00"},{"alias_kind":"pith_short_12","alias_value":"PKPNZXFEGDIM","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PKPNZXFEGDIMBMH7","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PKPNZXFE","created_at":"2026-05-18T12:27:54.935989+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/PKPNZXFEGDIMBMH7SLAB4TXQVQ","json":"https://pith.science/pith/PKPNZXFEGDIMBMH7SLAB4TXQVQ.json","graph_json":"https://pith.science/api/pith-number/PKPNZXFEGDIMBMH7SLAB4TXQVQ/graph.json","events_json":"https://pith.science/api/pith-number/PKPNZXFEGDIMBMH7SLAB4TXQVQ/events.json","paper":"https://pith.science/paper/PKPNZXFE"},"agent_actions":{"view_html":"https://pith.science/pith/PKPNZXFEGDIMBMH7SLAB4TXQVQ","download_json":"https://pith.science/pith/PKPNZXFEGDIMBMH7SLAB4TXQVQ.json","view_paper":"https://pith.science/paper/PKPNZXFE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.1663&json=true","fetch_graph":"https://pith.science/api/pith-number/PKPNZXFEGDIMBMH7SLAB4TXQVQ/graph.json","fetch_events":"https://pith.science/api/pith-number/PKPNZXFEGDIMBMH7SLAB4TXQVQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PKPNZXFEGDIMBMH7SLAB4TXQVQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PKPNZXFEGDIMBMH7SLAB4TXQVQ/action/storage_attestation","attest_author":"https://pith.science/pith/PKPNZXFEGDIMBMH7SLAB4TXQVQ/action/author_attestation","sign_citation":"https://pith.science/pith/PKPNZXFEGDIMBMH7SLAB4TXQVQ/action/citation_signature","submit_replication":"https://pith.science/pith/PKPNZXFEGDIMBMH7SLAB4TXQVQ/action/replication_record"}},"created_at":"2026-05-18T03:05:26.591231+00:00","updated_at":"2026-05-18T03:05:26.591231+00:00"}