{"id":"W3126518128","doi":"10.4153/s0008439521000059","title":"A multiplicative dual of nil-clean rings","year":2021,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"Memorial University of Newfoundland","funders":"","keywords":"Mathematics; Idempotence; Multiplicative function; Nilpotent; Dual (grammatical number); Pure mathematics; Order (exchange); Mathematical analysis","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0003577576,0.0002299274,0.0005063976,0.0001156497,0.0001057381,0.00004137232,0.0002364237,0.0001437361,0.01222694],"category_scores_gemma":[0.002484533,0.0002231499,0.000173263,0.0002054169,0.0002001398,0.00002998631,0.00007876521,0.0002383805,0.002995612],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001201426,"about_ca_system_score_gemma":0.0002947351,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000513597,"about_ca_topic_score_gemma":0.001639434,"domain_scores_codex":[0.9981942,0.00007596232,0.0005487499,0.000372676,0.0002840859,0.0005242995],"domain_scores_gemma":[0.9977755,0.0006567005,0.0001440178,0.0006254552,0.0002120566,0.0005863029],"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":[0.0000085053,0.0002556789,0.000127065,0.000627483,0.0001094326,0.0002433467,0.002307263,0.000001133211,0.0009810338,0.9444172,0.04871658,0.002205237],"study_design_scores_gemma":[0.0009378535,0.00007032332,0.0005982865,0.000564618,0.0001172723,0.0002253407,0.002650781,0.0002181505,0.02722388,0.8925184,0.0741842,0.0006909089],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9002279,0.0001331336,0.00283793,0.006927936,0.000103885,0.0004712553,0.00008460349,0.0001171272,0.08909623],"genre_scores_gemma":[0.9619881,0.000009636228,0.02822011,0.0006490294,0.0001317334,0.00004177171,0.00001110559,0.00007429296,0.008874204],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08022203,"threshold_uncertainty_score":0.9977807,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0293952888096729,"score_gpt":0.2597936500260908,"score_spread":0.2303983612164179,"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."}}