{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PKPNZXFEGDIMBMH7SLAB4TXQVQ","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":"341af9829507af063d25de0e0ec7ad50186fbad9347a0361208fcad9de2268c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-12-05T20:01:07Z","title_canon_sha256":"630b6cdfb2d208a13014a79ab9a7343f49b6f54d54fd6f74a577fc203ac3e7bf"},"schema_version":"1.0","source":{"id":"1312.1663","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1663","created_at":"2026-05-18T03:05:26Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1663v1","created_at":"2026-05-18T03:05:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1663","created_at":"2026-05-18T03:05:26Z"},{"alias_kind":"pith_short_12","alias_value":"PKPNZXFEGDIM","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PKPNZXFEGDIMBMH7","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PKPNZXFE","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:13578c9c547b854273edc82f6fc173fdfc598cd543c20520968c4a5ecefba41c","target":"graph","created_at":"2026-05-18T03:05:26Z","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":"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 $S$.","authors_text":"Leonard D\\u{a}u\\c{s}, Mohamed A. Salim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-12-05T20:01:07Z","title":"From regular modules to von Neumann regular rings via coordinatization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1663","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":"sha256:00ac3038a074d5a7720baabd598e66984fe9fc40cf3aa78293f52b96e9974247","target":"record","created_at":"2026-05-18T03:05:26Z","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":"341af9829507af063d25de0e0ec7ad50186fbad9347a0361208fcad9de2268c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-12-05T20:01:07Z","title_canon_sha256":"630b6cdfb2d208a13014a79ab9a7343f49b6f54d54fd6f74a577fc203ac3e7bf"},"schema_version":"1.0","source":{"id":"1312.1663","kind":"arxiv","version":1}},"canonical_sha256":"7a9edcdca430d0c0b0ff92c01e4ef0ac3aa4c0287475a80e50f9a0362b167c96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a9edcdca430d0c0b0ff92c01e4ef0ac3aa4c0287475a80e50f9a0362b167c96","first_computed_at":"2026-05-18T03:05:26.591153Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:26.591153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nvSuddfYCERLRaeS3USdMRL5lpZHe3sNPoW1EkwhfL6ZWRihgDhncnosons44ZEqm/Vpr0kOdGXtWaXjmCiZDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:26.591716Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1663","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00ac3038a074d5a7720baabd598e66984fe9fc40cf3aa78293f52b96e9974247","sha256:13578c9c547b854273edc82f6fc173fdfc598cd543c20520968c4a5ecefba41c"],"state_sha256":"9ab4638e34dcc2690a221c8ac7415c87dd7176eb3a6af3a2e2f699699814c49b"}