{"id":"W4205613664","doi":"10.1016/s0024-3795(03)00721-3","title":"Burnside's theorem for matrix rings over division rings*1","year":2004,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Subalgebra; Rank (graph theory); Division ring; Division algebra; Ring (chemistry); Counterexample; Transitive relation; Matrix (chemical analysis); Pure mathematics; Field (mathematics); Combinatorics; Matrix ring; Division (mathematics); Discrete mathematics; Algebra over a field; Arithmetic","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001511801,0.0001793526,0.0002033287,0.00006476593,0.0002733585,0.00003911428,0.0001921823,0.00009055657,0.00004482445],"category_scores_gemma":[0.0001942802,0.0001622203,0.0000764596,0.0001641597,0.00005806388,0.0001501074,0.0001115759,0.000150754,0.00005120757],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003968245,"about_ca_system_score_gemma":0.00002438094,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002671927,"about_ca_topic_score_gemma":0.000003443548,"domain_scores_codex":[0.9989275,0.000008967363,0.0003009349,0.0003538885,0.0001552295,0.0002534888],"domain_scores_gemma":[0.9989356,0.0003401929,0.0001307366,0.000388617,0.00009909728,0.0001056911],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000005367607,0.00007691071,0.00004050152,0.00008149681,0.00001332202,4.23674e-7,0.0001624502,0.00001712785,0.001403628,0.9968379,0.00009160855,0.00126923],"study_design_scores_gemma":[0.0006708657,0.00004003995,0.0002272198,0.00004014402,0.00003210089,0.000008863269,0.00003855638,0.0003386078,0.006180564,0.9702405,0.02198315,0.0001993764],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3441356,0.0004245283,0.6506345,0.001044034,0.00006272298,0.001669237,0.00005986371,0.0002888062,0.001680647],"genre_scores_gemma":[0.809341,0.0001022555,0.1875683,0.0002579176,0.0004148239,0.0006179004,0.00002905717,0.00007828392,0.001590446],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.4652054,"threshold_uncertainty_score":0.6615151,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02657018408386946,"score_gpt":0.3440714158987657,"score_spread":0.3175012318148963,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}