{"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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0008221544,0.0003447004,0.0007638973,0.0003423244,0.0002242237,0.0003163593,0.0006294213,0.0001855892,0.0006386716],"category_scores_gemma":[0.0007617662,0.0003005074,0.0005149774,0.0001685057,0.0001193422,0.001099024,0.0002116774,0.0006662477,0.00005357029],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001552277,"about_ca_system_score_gemma":0.00009501155,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00007994621,"about_ca_topic_score_gemma":0.00005295611,"domain_scores_codex":[0.9970679,0.0001310691,0.001139175,0.0002849963,0.0008463972,0.0005304911],"domain_scores_gemma":[0.9976744,0.0003449031,0.001142725,0.0003727301,0.0001617259,0.0003034899],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"observational","study_design_scores_codex":[0.002815264,0.002976636,0.1524951,0.001659779,0.003033206,0.0004639709,0.01289144,0.00003773055,0.2389947,0.2501474,0.2723287,0.06215604],"study_design_scores_gemma":[0.02060559,0.001892629,0.5058446,0.001757807,0.001590301,0.001714207,0.0006029027,0.001203535,0.06440789,0.3678535,0.02939139,0.003135693],"study_design_candidate":"observational","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9886444,0.00007748128,0.007879997,0.0002951738,0.0018254,0.0001247881,0.000003918685,0.0000565496,0.001092331],"genre_scores_gemma":[0.9912571,0.00002942854,0.004085546,0.000209738,0.003974177,0.000002214085,9.528161e-7,0.00007004032,0.000370833],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3533494,"threshold_uncertainty_score":0.9999447,"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."}}