{"id":"W2084535267","doi":"10.1556/sscmath.2007.1019","title":"Conditions for rings to be finite or have only central zero divisors","year":2007,"lang":"en","type":"article","venue":"Studia Scientiarum Mathematicarum Hungarica","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Brock University","funders":"","keywords":"Mathematics; Subring; Zero (linguistics); Zero divisor; Pure mathematics; Ring (chemistry)","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.002082307,0.0005366022,0.0008424287,0.0005104578,0.001082211,0.0002966612,0.0008357795,0.0001605749,0.0002868504],"category_scores_gemma":[0.003637046,0.0004434367,0.0004076206,0.0008164771,0.0003281702,0.000284487,0.000427323,0.0002865894,0.0001670316],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000176821,"about_ca_system_score_gemma":0.0002436981,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001375321,"about_ca_topic_score_gemma":0.0003556574,"domain_scores_codex":[0.9951192,0.00005422237,0.001114006,0.0009249822,0.0009686999,0.001818945],"domain_scores_gemma":[0.995001,0.002731313,0.0003857821,0.0009493881,0.0002939625,0.0006385586],"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":[0.0001926326,0.002266566,0.001564596,0.000987864,0.0005951964,0.00005789238,0.02411444,0.00003339213,0.002211393,0.8205465,0.1458689,0.001560617],"study_design_scores_gemma":[0.003977448,0.001089412,0.007870961,0.0007751139,0.001108361,0.0001007735,0.0096701,0.001302696,0.01269474,0.8861157,0.07264073,0.002654016],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5306168,0.00006443967,0.4271511,0.005246272,0.001713661,0.004785768,0.0004427677,0.0008007026,0.02917842],"genre_scores_gemma":[0.9048142,0.000007428866,0.08210804,0.001016614,0.0002706088,0.000216899,0.00003137009,0.0001367305,0.01139812],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3741973,"threshold_uncertainty_score":0.9998018,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05602291501112624,"score_gpt":0.3279861124820258,"score_spread":0.2719631974708996,"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."}}