{"id":"W2022862970","doi":"10.1007/s00605-007-0505-1","title":"Extremely noncommutative elements in rings","year":2007,"lang":"de","type":"article","venue":"Monatshefte für Mathematik","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"Brock University","funders":"","keywords":"Centralizer and normalizer; Subring; Noncommutative geometry; Mathematics; Commutative property; Pure mathematics; Ring (chemistry); Noncommutative ring; Element (criminal law); Algebra over a field; Chemistry; Law","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":[0.001838951,0.0005157829,0.0006929853,0.001473923,0.001485673,0.003019661,0.0005870171,0.0007611194,0.004698245],"category_scores_gemma":[0.003629184,0.0004340606,0.00039909,0.001019882,0.004551127,0.00638267,0.002398239,0.002218564,0.0006251605],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008282994,"about_ca_system_score_gemma":0.0003857331,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001403464,"about_ca_topic_score_gemma":0.0001777873,"domain_scores_codex":[0.9988819,0.0003949011,0.00006093337,0.0001698743,0.0003552167,0.0001371882],"domain_scores_gemma":[0.9978831,0.001182829,0.0002081842,0.0002011119,0.0002332258,0.0002914794],"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":[0.00001965864,0.000008026002,0.0001552272,0.00002028505,0.000003870964,0.00004302859,0.0002697237,0.000157484,0.0005384102,0.9971284,0.0003269133,0.001328891],"study_design_scores_gemma":[0.00001182046,0.00001607799,0.0002838365,0.000006610703,0.000005560917,0.0001257196,0.0001046391,0.0005070855,0.0003859109,0.9953172,0.003229491,0.00000605266],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7619529,0.00735493,0.09629264,0.004474154,0.0007727485,0.00004174181,0.0001907037,0.0002028093,0.1287173],"genre_scores_gemma":[0.9744645,0.001206027,0.008496021,0.0002179575,0.0007849895,0.00004089357,0.00006169841,0.00003084154,0.01469699],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004698245,"threshold_uncertainty_score":0.01571721,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03775560450178634,"score_gpt":0.3200208131811158,"score_spread":0.2822652086793295,"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."}}