{"id":"W69397485","doi":"10.1007/978-3-0346-0286-0_22","title":"On Clean Group Rings","year":2010,"lang":"en","type":"book-chapter","venue":"Birkhäuser Basel eBooks","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":16,"is_retracted":false,"has_abstract":true,"ca_institutions":"Memorial University of Newfoundland","funders":"","keywords":"Ring (chemistry); Group ring; Group (periodic table); Unit (ring theory); Idempotence; Mathematics; Order (exchange); Pure mathematics; Algebra over a field; Combinatorics; Chemistry; Mathematics education","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":[0.0003720554,0.0004808843,0.0003768078,0.001335392,0.0009457393,0.001366569,0.0003197464,0.0004303915,0.009092002],"category_scores_gemma":[0.0006303978,0.0002773209,0.0003206072,0.001265143,0.001772875,0.003837039,0.001329477,0.001267007,0.003759706],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005774373,"about_ca_system_score_gemma":0.0003366174,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003738788,"about_ca_topic_score_gemma":0.0004955376,"domain_scores_codex":[0.9997513,0.00004750976,0.00001028902,0.00004755772,0.0001128756,0.00003050357],"domain_scores_gemma":[0.9998065,0.00007046184,0.000015662,0.00004940939,0.00003901596,0.0000190427],"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":[0.00001063442,0.000009058506,0.00006235408,0.0001230472,0.000005017738,0.0000630215,0.0002826971,0.0003649023,0.001077827,0.9516355,0.01560741,0.03075841],"study_design_scores_gemma":[0.000003574761,0.0000186063,0.0004418094,0.0000715135,0.000009501699,0.0003507283,0.0001162666,0.0006166357,0.001042586,0.72041,0.2769078,0.00001096881],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.02414213,0.06586021,0.08708082,0.002631332,0.001778529,0.00006071462,0.0005111673,0.0005134068,0.8174217],"genre_scores_gemma":[0.3093208,0.06665359,0.06353074,0.002588422,0.004082053,0.0001360889,0.0007316956,0.0003836706,0.5525729],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.009092002,"threshold_uncertainty_score":0.03041577,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03864685847984361,"score_gpt":0.2533295046481724,"score_spread":0.2146826461683288,"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."}}