{"id":"W7106343978","doi":"10.1142/s0219498827501039","title":"When every S-finite ideal is finitely generated","year":2025,"lang":"en","type":"article","venue":"Journal of Algebra and Its Applications","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"St. Francis Xavier University","funders":"","keywords":"Ideal (ethics); Finitely-generated abelian group; Class (philosophy); Property (philosophy); Ring (chemistry); Commutative ring; Commutative property; Algebra over a field; Noetherian ring","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":[],"consensus_categories":[],"category_scores_codex":[0.000289268,0.00014075,0.0002838511,0.0002205288,0.0001841862,0.00008438396,0.0002260324,0.00009116561,0.0001160329],"category_scores_gemma":[0.0001647446,0.000118372,0.000106005,0.0002636453,0.00004044027,0.0001950063,0.00005343112,0.0002350938,0.00002503457],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000268583,"about_ca_system_score_gemma":0.0001283415,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002911906,"about_ca_topic_score_gemma":0.000002772503,"domain_scores_codex":[0.9988698,0.00003169768,0.0005833129,0.0001585965,0.0001868055,0.0001697318],"domain_scores_gemma":[0.9986483,0.0003792138,0.0003345384,0.0002084917,0.0003227161,0.0001067397],"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":[0.00004792052,0.0003734824,0.0006551875,0.0002179894,0.0003786083,0.000008113665,0.001263499,0.00001077718,0.006236909,0.8418869,0.1308229,0.0180977],"study_design_scores_gemma":[0.0008044515,0.0000754416,0.0019583,0.0001388969,0.0002162806,0.00005065053,0.0001912449,0.0004578054,0.008595,0.8471556,0.1401306,0.0002257277],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9198171,0.005880019,0.05702681,0.008560655,0.0002677257,0.0005636382,0.00003898915,0.0000725529,0.007772428],"genre_scores_gemma":[0.9760792,0.001661461,0.01358194,0.002418068,0.0005765997,0.0000458151,0.000006053733,0.00003439137,0.00559646],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05626203,"threshold_uncertainty_score":0.4827071,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03417723154699224,"score_gpt":0.2938559750102878,"score_spread":0.2596787434632955,"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."}}