{"id":"W2009709555","doi":"10.1080/03081080802167880","title":"On irreducible and transitive subalgebras in matrix algebras","year":2008,"lang":"en","type":"article","venue":"Linear and Multilinear Algebra","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"Memorial University of Newfoundland","funders":"National Center for Theoretical Sciences","keywords":"Subring; Centralizer and normalizer; Mathematics; Subalgebra; Division ring; Combinatorics; Ring (chemistry); Rank (graph theory); Zero (linguistics); Transitive relation; Discrete mathematics; Pure mathematics; Algebra over a field; Division (mathematics); 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001784659,0.0007381781,0.0005698405,0.001624647,0.001951106,0.002186894,0.0005509119,0.0005488665,0.003904671],"category_scores_gemma":[0.002052268,0.0004559131,0.001056476,0.001369845,0.003273069,0.004059316,0.002185271,0.001789976,0.001006562],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001474158,"about_ca_system_score_gemma":0.0008488423,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001682292,"about_ca_topic_score_gemma":0.001900547,"domain_scores_codex":[0.9986903,0.000382833,0.0001039855,0.0001702849,0.0003874681,0.0002651385],"domain_scores_gemma":[0.9987325,0.0003959813,0.0002441795,0.0001295622,0.0002286603,0.0002690856],"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":[0.00002831833,0.00002979816,0.0001977595,0.00004298472,0.00000536815,0.0001506858,0.000676289,0.0006793757,0.001559441,0.9923397,0.0006231238,0.003667184],"study_design_scores_gemma":[0.00001339339,0.00005439734,0.0003252933,0.00002281386,0.000007951811,0.000215198,0.000215976,0.004989708,0.0008969144,0.9889894,0.004254659,0.00001432469],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5225214,0.0104076,0.2288884,0.002542864,0.0006636516,0.0001959196,0.0005789179,0.0005280335,0.2336733],"genre_scores_gemma":[0.9388735,0.003502625,0.03770185,0.0003782375,0.000985468,0.0001360069,0.0004458615,0.00008493508,0.01789136],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003904671,"threshold_uncertainty_score":0.01306242,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.041974909956296,"score_gpt":0.3355522218027743,"score_spread":0.2935773118464783,"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."}}