{"id":"W1994755797","doi":"10.1016/s0022-4049(98)00129-7","title":"Study of modules over formal triangular matrix rings","year":2000,"lang":"en","type":"article","venue":"Journal of Pure and Applied Algebra","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":76,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Calgary","funders":"University of Calgary","keywords":"Mathematics; Projective test; Cover (algebra); Projective module; Generator (circuit theory); Matrix (chemical analysis); Pure mathematics; Dual (grammatical number); Finitely-generated abelian group; Projective cover; Basis (linear algebra); Flat module; Discrete mathematics; Algebra over a field; Combinatorics; Projective space; Collineation; Power (physics); Geometry","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008286455,0.0004544591,0.0005627424,0.001284695,0.001014565,0.002280043,0.0008847425,0.0005753444,0.008450104],"category_scores_gemma":[0.00290339,0.0002677903,0.0004803304,0.001151497,0.002113281,0.004080286,0.0009547576,0.0009639233,0.0003972479],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008471548,"about_ca_system_score_gemma":0.0005834511,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007064605,"about_ca_topic_score_gemma":0.0007545383,"domain_scores_codex":[0.9996824,0.0001038521,0.00001241822,0.00005125519,0.00007346911,0.00007670314],"domain_scores_gemma":[0.9986445,0.0006999358,0.0001513622,0.00008618974,0.0001895567,0.0002285181],"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":[0.00003667347,0.00003550283,0.0007203844,0.00005817987,0.000009176074,0.0001342678,0.0004773808,0.0012371,0.0009072825,0.9927217,0.0006310444,0.003031141],"study_design_scores_gemma":[0.00003473976,0.00006656432,0.001047802,0.00003318598,0.00002242756,0.0005412397,0.0005125226,0.01654843,0.002219362,0.9733201,0.00563363,0.00001985742],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8820475,0.002447762,0.04638472,0.001585285,0.0001197434,0.00004706348,0.0001447037,0.0001006767,0.06712257],"genre_scores_gemma":[0.9841113,0.0005003599,0.003889435,0.00006873925,0.0001444402,0.00001115008,0.00008473347,0.00002298527,0.01116684],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.008450104,"threshold_uncertainty_score":0.0282684,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0185971037634065,"score_gpt":0.271617375161457,"score_spread":0.2530202713980505,"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."}}