{"id":"W3083632620","doi":"10.1142/s021949882250013x","title":"Rings with fine idempotents","year":2020,"lang":"en","type":"article","venue":"Journal of Algebra and Its Applications","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"Memorial University of Newfoundland","funders":"Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Idempotence; Ring (chemistry); Simple ring; Primitive ring; Von Neumann regular ring; Unit (ring theory); Simple (philosophy); Diagonal; Integer (computer science); Combinatorics; Matrix ring; Pure mathematics; Nilpotent; Principal ideal ring; Matrix (chemical analysis); Commutative ring; Invertible matrix; Geometry","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":[],"consensus_categories":[],"category_scores_codex":[0.0001158563,0.0001017531,0.0002150543,0.00004609516,0.00009405344,0.00003797216,0.0001580382,0.00003585577,0.00004229629],"category_scores_gemma":[0.00008564181,0.00007262246,0.00005020464,0.0001544602,0.00003029178,0.0001790552,0.00003126714,0.0001742317,0.00001673444],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000009235832,"about_ca_system_score_gemma":0.00003436519,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":6.276682e-7,"about_ca_topic_score_gemma":0.000001170865,"domain_scores_codex":[0.9992309,0.00001172336,0.0003301654,0.0001173056,0.0001930155,0.0001169568],"domain_scores_gemma":[0.9991615,0.00009216402,0.0003083478,0.00009920867,0.0001524126,0.0001863314],"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":[0.0002062829,0.0006172449,0.004289508,0.0005829044,0.0005167003,0.00004366655,0.003699544,0.00002608893,0.01933463,0.9196485,0.02590749,0.02512746],"study_design_scores_gemma":[0.006686607,0.002156018,0.02583514,0.0005498946,0.001016645,0.001251031,0.001438957,0.001121734,0.03508522,0.7027591,0.2207174,0.001382224],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9702665,0.0006496581,0.02023892,0.00756289,0.00002050258,0.0002367456,0.00000529274,0.00003004279,0.0009894192],"genre_scores_gemma":[0.9910839,0.0001556777,0.007764992,0.0004775335,0.0003478322,0.00001098104,9.511031e-7,0.00001985197,0.0001382919],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2168894,"threshold_uncertainty_score":0.2961458,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03448564168472027,"score_gpt":0.2716022581226765,"score_spread":0.2371166164379563,"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."}}