{"id":"W2950093129","doi":"10.1016/j.jalgebra.2014.09.039","title":"Differential polynomial rings over rings satisfying a polynomial identity","year":2014,"lang":"en","type":"article","venue":"Journal of Algebra","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":16,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Locally nilpotent; Nilpotent; Polynomial; Identity (music); Jacobson radical; Polynomial ring; Ring (chemistry); Differential (mechanical device); Combinatorics; Pure mathematics; Discrete mathematics; Nilpotent group; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"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":[0.002585679,0.0007202468,0.001464832,0.001335087,0.002513753,0.004595004,0.001164281,0.001204274,0.007024975],"category_scores_gemma":[0.004363583,0.0007574733,0.001102536,0.001679447,0.004233708,0.00899364,0.003792295,0.003277601,0.001556048],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001275388,"about_ca_system_score_gemma":0.001362904,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004486908,"about_ca_topic_score_gemma":0.000380675,"domain_scores_codex":[0.9976928,0.0004701517,0.0001806529,0.0004864961,0.0006149359,0.0005550505],"domain_scores_gemma":[0.9970837,0.00111659,0.0003893658,0.0003972713,0.0004648494,0.0005481314],"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":[0.00006937698,0.00004197217,0.0003523852,0.00003192192,0.00001124015,0.0001911875,0.0003252435,0.0001943437,0.001343572,0.993304,0.0008764211,0.003258279],"study_design_scores_gemma":[0.00006494618,0.00006126077,0.0004146608,0.00001118572,0.00002977281,0.000588785,0.000238786,0.001706805,0.002340685,0.9894814,0.005041941,0.00001973177],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.562288,0.00118774,0.2306576,0.0038994,0.0007696343,0.0001349992,0.0007127624,0.0008794472,0.1994703],"genre_scores_gemma":[0.9649981,0.0005691808,0.01341694,0.0003460054,0.0005647094,0.00003661252,0.0002968173,0.00008789238,0.01968372],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007024975,"threshold_uncertainty_score":0.02350086,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02113901047120314,"score_gpt":0.2796633992247007,"score_spread":0.2585243887534975,"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."}}