{"id":"W2056100933","doi":"10.1016/s0021-8693(02)00562-8","title":"Engel varieties of associative rings and the number of Mersenne primes","year":2003,"lang":"en","type":"article","venue":"Journal of Algebra","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":false,"ca_institutions":"Western University","funders":"","keywords":"Mathematics; Nilpotent; Semigroup; Pure mathematics; Associative property; Mersenne prime; Ring (chemistry); Discrete mathematics","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":[0.003337968,0.0009646969,0.00162252,0.004558973,0.003862294,0.007321656,0.001723157,0.001770901,0.009382467],"category_scores_gemma":[0.008967901,0.0008947495,0.0008582285,0.002361933,0.009126711,0.01305341,0.003482512,0.003335412,0.0008996488],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001844984,"about_ca_system_score_gemma":0.0007648807,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004183785,"about_ca_topic_score_gemma":0.0004191268,"domain_scores_codex":[0.9986822,0.000414083,0.00009342865,0.000267239,0.0002565313,0.0002864397],"domain_scores_gemma":[0.9929137,0.003941994,0.001105163,0.0005002847,0.0004273014,0.001111465],"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":[0.0001346005,0.00002366781,0.0006769361,0.0000292259,0.00001030211,0.00008412546,0.0003119973,0.0006425215,0.0003911371,0.9944625,0.0004402494,0.002792584],"study_design_scores_gemma":[0.00002584175,0.00001730473,0.0003537601,0.0000144389,0.000009838794,0.0001135361,0.0001447198,0.0009413714,0.0003988706,0.9967032,0.0012624,0.00001457167],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8272213,0.003592541,0.03727642,0.004506194,0.0004709576,0.00005309606,0.0002869254,0.000239035,0.1263535],"genre_scores_gemma":[0.9871327,0.0006945394,0.003461941,0.00009536725,0.0002566,0.00002681568,0.00008230498,0.00002635145,0.008223378],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009382467,"threshold_uncertainty_score":0.03138745,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01970841359953279,"score_gpt":0.306133477586855,"score_spread":0.2864250639873222,"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."}}