{"id":"W1969868531","doi":"10.1006/jabr.2001.8971","title":"Embedding Noetherian Rings in Artinian Rings","year":2001,"lang":"en","type":"article","venue":"Journal of Algebra","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Manitoba","funders":"","keywords":"Mathematics; Artinian ring; Noetherian; Semisimple module; Radical of a ring; Pure mathematics; Embedding; Noncommutative ring; Discrete mathematics; Ring (chemistry); Commutative ring; Principal ideal ring; Algebra over a field; Commutative property; Computer science","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001174903,0.0005199832,0.0004796441,0.001354972,0.001323874,0.004015235,0.0005604551,0.0006303567,0.004462766],"category_scores_gemma":[0.001759165,0.0005035686,0.0004273843,0.0006819259,0.002643328,0.007819306,0.002665165,0.002322491,0.0006860684],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008569248,"about_ca_system_score_gemma":0.0004062761,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004181026,"about_ca_topic_score_gemma":0.0006981911,"domain_scores_codex":[0.9992501,0.0002286277,0.00005291875,0.0001357114,0.0001805667,0.0001519902],"domain_scores_gemma":[0.9989482,0.000296257,0.0001635055,0.0001717201,0.0001435814,0.0002767712],"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":[0.00005210919,0.00003520572,0.000333306,0.00002497803,0.000007201071,0.00006956905,0.0005978299,0.0004215151,0.001334865,0.9913186,0.000428367,0.005376327],"study_design_scores_gemma":[0.00001719889,0.0000357149,0.0005470907,0.00001343484,0.00001103479,0.0001140316,0.0004257162,0.001528835,0.0009193838,0.9888882,0.007487776,0.00001155445],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6496308,0.005433457,0.1417011,0.003840214,0.0011235,0.00007273313,0.0002676214,0.0004475094,0.1974829],"genre_scores_gemma":[0.9679152,0.0009819469,0.01272582,0.0001556264,0.0003325157,0.00001778299,0.00008187465,0.00004663591,0.01774258],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004462766,"threshold_uncertainty_score":0.01492947,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03362976916202103,"score_gpt":0.3065470046026969,"score_spread":0.2729172354406759,"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."}}