{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:6F2BCAW4YS7V3PNXBNEDJU7WYG","short_pith_number":"pith:6F2BCAW4","schema_version":"1.0","canonical_sha256":"f1741102dcc4bf5dbdb70b4834d3f6c18ae1e13338b8674337dab283ef560509","source":{"kind":"arxiv","id":"1907.05335","version":1},"attestation_state":"computed","paper":{"title":"On a special presentation of matrix algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Geir Agnarsson, Samuel S. Mendelson","submitted_at":"2019-07-11T16:10:15Z","abstract_excerpt":"Recognizing when a ring is a complete matrix ring is of significant importance in algebra. It is well-known folklore that a ring $R$ is a complete $n\\times n$ matrix ring, so $R\\cong M_{n}(S)$ for some ring $S$, if and only if it contains a set of $n\\times n$ matrix units $\\{e_{ij}\\}_{i,j=1}^n$. A more recent and less known result states that a ring $R$ is a complete $(m+n)\\times(m+n)$ matrix ring if and only if, $R$ contains three elements, $a$, $b$, and $f$, satisfying the two relations $af^m+f^nb=1$ and $f^{m+n}=0$. In many instances the two elements $a$ and $b$ can be replaced by appropria"},"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":"1907.05335","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-07-11T16:10:15Z","cross_cats_sorted":[],"title_canon_sha256":"0bba761d55d59bf5b41476125e08840dcd02cabca2eec9e2388cc33c57a5aa75","abstract_canon_sha256":"82d8cddde928591ea5cb4079fc7f61d94ee81fc98811b1e23aad9e11b6143d50"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:50.702346Z","signature_b64":"N0iyodyRcDd+n00zmfVj6vu7P2G3H8KST/yNSbCtKpBf7qgssIepEce90zTef3PhRYgq3gxXs0UHvBC48y63Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1741102dcc4bf5dbdb70b4834d3f6c18ae1e13338b8674337dab283ef560509","last_reissued_at":"2026-05-17T23:40:50.701618Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:50.701618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a special presentation of matrix algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Geir Agnarsson, Samuel S. Mendelson","submitted_at":"2019-07-11T16:10:15Z","abstract_excerpt":"Recognizing when a ring is a complete matrix ring is of significant importance in algebra. It is well-known folklore that a ring $R$ is a complete $n\\times n$ matrix ring, so $R\\cong M_{n}(S)$ for some ring $S$, if and only if it contains a set of $n\\times n$ matrix units $\\{e_{ij}\\}_{i,j=1}^n$. A more recent and less known result states that a ring $R$ is a complete $(m+n)\\times(m+n)$ matrix ring if and only if, $R$ contains three elements, $a$, $b$, and $f$, satisfying the two relations $af^m+f^nb=1$ and $f^{m+n}=0$. In many instances the two elements $a$ and $b$ can be replaced by appropria"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05335","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":"1907.05335","created_at":"2026-05-17T23:40:50.701733+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.05335v1","created_at":"2026-05-17T23:40:50.701733+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.05335","created_at":"2026-05-17T23:40:50.701733+00:00"},{"alias_kind":"pith_short_12","alias_value":"6F2BCAW4YS7V","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"6F2BCAW4YS7V3PNX","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"6F2BCAW4","created_at":"2026-05-18T12:33:10.108867+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/6F2BCAW4YS7V3PNXBNEDJU7WYG","json":"https://pith.science/pith/6F2BCAW4YS7V3PNXBNEDJU7WYG.json","graph_json":"https://pith.science/api/pith-number/6F2BCAW4YS7V3PNXBNEDJU7WYG/graph.json","events_json":"https://pith.science/api/pith-number/6F2BCAW4YS7V3PNXBNEDJU7WYG/events.json","paper":"https://pith.science/paper/6F2BCAW4"},"agent_actions":{"view_html":"https://pith.science/pith/6F2BCAW4YS7V3PNXBNEDJU7WYG","download_json":"https://pith.science/pith/6F2BCAW4YS7V3PNXBNEDJU7WYG.json","view_paper":"https://pith.science/paper/6F2BCAW4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.05335&json=true","fetch_graph":"https://pith.science/api/pith-number/6F2BCAW4YS7V3PNXBNEDJU7WYG/graph.json","fetch_events":"https://pith.science/api/pith-number/6F2BCAW4YS7V3PNXBNEDJU7WYG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6F2BCAW4YS7V3PNXBNEDJU7WYG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6F2BCAW4YS7V3PNXBNEDJU7WYG/action/storage_attestation","attest_author":"https://pith.science/pith/6F2BCAW4YS7V3PNXBNEDJU7WYG/action/author_attestation","sign_citation":"https://pith.science/pith/6F2BCAW4YS7V3PNXBNEDJU7WYG/action/citation_signature","submit_replication":"https://pith.science/pith/6F2BCAW4YS7V3PNXBNEDJU7WYG/action/replication_record"}},"created_at":"2026-05-17T23:40:50.701733+00:00","updated_at":"2026-05-17T23:40:50.701733+00:00"}