{"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"}