{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MWDSZIJPIB7UBRUTSGVKQ4MA7Z","short_pith_number":"pith:MWDSZIJP","schema_version":"1.0","canonical_sha256":"65872ca12f407f40c69391aaa87180fe6ae6dea1545e821c8fd7e5d30a34d118","source":{"kind":"arxiv","id":"1507.00377","version":3},"attestation_state":"computed","paper":{"title":"Theorems of Burnside and Wedderburn revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Bamdad R. Yahaghi","submitted_at":"2015-07-01T21:23:19Z","abstract_excerpt":"We approach celebrated theorems of Burnside and Wedderburn via simultaneous triangularization. First, for a general field $F$, we prove that $M_n(F)$ is the only irrreducible subalgebra of triangularizable matrices in $M_n(F)$ provided such a subalgebra exists. This provides a slight generalization of a well-known theorem of Burnside. Next, for a given $n > 1$, we characterize all fields $F$ such that Burnside's Theorem holds in $M_n(F)$, i.e., $M_n(F)$ is the only irreducible subalgebra of itself. In fact, for a subfield $F$ of the center of a division ring $D$, our simple proof of the aforem"},"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":"1507.00377","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-07-01T21:23:19Z","cross_cats_sorted":[],"title_canon_sha256":"8647f3343380fd46a0f25e4800fddd2c591cffb9eb32ea2c7b2779a0372b4a44","abstract_canon_sha256":"3add52f92d3e68790ac835bb28a085c90e87f1666a7264b72c0db453b87db45b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:51.322919Z","signature_b64":"6UPYuCuu2tR/xpa7FBw1lw+tUwvaAk8stBohFL8XCdGyla645Z+FftLsQxJvXuel+auMBmraaDfRSE+VHHQPCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65872ca12f407f40c69391aaa87180fe6ae6dea1545e821c8fd7e5d30a34d118","last_reissued_at":"2026-05-18T00:47:51.322129Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:51.322129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Theorems of Burnside and Wedderburn revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Bamdad R. Yahaghi","submitted_at":"2015-07-01T21:23:19Z","abstract_excerpt":"We approach celebrated theorems of Burnside and Wedderburn via simultaneous triangularization. First, for a general field $F$, we prove that $M_n(F)$ is the only irrreducible subalgebra of triangularizable matrices in $M_n(F)$ provided such a subalgebra exists. This provides a slight generalization of a well-known theorem of Burnside. Next, for a given $n > 1$, we characterize all fields $F$ such that Burnside's Theorem holds in $M_n(F)$, i.e., $M_n(F)$ is the only irreducible subalgebra of itself. In fact, for a subfield $F$ of the center of a division ring $D$, our simple proof of the aforem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00377","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":"1507.00377","created_at":"2026-05-18T00:47:51.322251+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.00377v3","created_at":"2026-05-18T00:47:51.322251+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00377","created_at":"2026-05-18T00:47:51.322251+00:00"},{"alias_kind":"pith_short_12","alias_value":"MWDSZIJPIB7U","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MWDSZIJPIB7UBRUT","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MWDSZIJP","created_at":"2026-05-18T12:29:32.376354+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/MWDSZIJPIB7UBRUTSGVKQ4MA7Z","json":"https://pith.science/pith/MWDSZIJPIB7UBRUTSGVKQ4MA7Z.json","graph_json":"https://pith.science/api/pith-number/MWDSZIJPIB7UBRUTSGVKQ4MA7Z/graph.json","events_json":"https://pith.science/api/pith-number/MWDSZIJPIB7UBRUTSGVKQ4MA7Z/events.json","paper":"https://pith.science/paper/MWDSZIJP"},"agent_actions":{"view_html":"https://pith.science/pith/MWDSZIJPIB7UBRUTSGVKQ4MA7Z","download_json":"https://pith.science/pith/MWDSZIJPIB7UBRUTSGVKQ4MA7Z.json","view_paper":"https://pith.science/paper/MWDSZIJP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.00377&json=true","fetch_graph":"https://pith.science/api/pith-number/MWDSZIJPIB7UBRUTSGVKQ4MA7Z/graph.json","fetch_events":"https://pith.science/api/pith-number/MWDSZIJPIB7UBRUTSGVKQ4MA7Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MWDSZIJPIB7UBRUTSGVKQ4MA7Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MWDSZIJPIB7UBRUTSGVKQ4MA7Z/action/storage_attestation","attest_author":"https://pith.science/pith/MWDSZIJPIB7UBRUTSGVKQ4MA7Z/action/author_attestation","sign_citation":"https://pith.science/pith/MWDSZIJPIB7UBRUTSGVKQ4MA7Z/action/citation_signature","submit_replication":"https://pith.science/pith/MWDSZIJPIB7UBRUTSGVKQ4MA7Z/action/replication_record"}},"created_at":"2026-05-18T00:47:51.322251+00:00","updated_at":"2026-05-18T00:47:51.322251+00:00"}