{"id":"W2028704409","doi":"10.1155/ijmms.2005.1387","title":"A weak periodicity condition for rings","year":2005,"lang":"en","type":"article","venue":"International Journal of Mathematics and Mathematical Sciences","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Brock University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Element (criminal law); Nilpotent; Commutative property; Jacobson radical; Ring (chemistry); Pure mathematics; Center (category theory); Algebra over a field; Discrete mathematics; Law; Crystallography","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":[0.001414125,0.0001404765,0.0003232961,0.0001510127,0.000131278,0.0001519218,0.0005070437,0.00005889011,0.0002132287],"category_scores_gemma":[0.002197156,0.0001000915,0.000132057,0.00007636317,0.0003386906,0.0004038194,0.00008757761,0.0001270506,0.00001113387],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005898537,"about_ca_system_score_gemma":0.00005431927,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":3.560694e-7,"about_ca_topic_score_gemma":0.000001945981,"domain_scores_codex":[0.9981791,0.00001507031,0.0007533465,0.0001435104,0.0007172107,0.000191808],"domain_scores_gemma":[0.9974463,0.001361319,0.0005984277,0.00009634258,0.0003913801,0.0001062212],"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":[0.000008694779,0.0002546851,0.00002201116,0.00008713952,0.00005197188,0.000002401303,0.0007648182,0.000008415838,0.0005145817,0.9923421,0.0004484853,0.005494731],"study_design_scores_gemma":[0.0005250133,0.0001423833,0.00001638929,0.0002218982,0.00003925268,0.0003472684,0.0006911029,0.004252241,0.001410359,0.9882013,0.004032515,0.0001202973],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"methods","genre_scores_codex":[0.5121717,0.00009889039,0.4749461,0.004846556,0.0003252829,0.000295302,0.00001026309,0.00003186392,0.007274027],"genre_scores_gemma":[0.3327375,0.00003580712,0.6665093,0.000108165,0.0003798445,0.000009858109,4.054739e-7,0.00001176741,0.0002073227],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.1915632,"threshold_uncertainty_score":0.4081614,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05500801636814043,"score_gpt":0.3874104494105624,"score_spread":0.332402433042422,"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."}}