{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005733859,0.0002029404,0.0005960613,0.0001472618,0.00009561611,0.00005039254,0.0002281373,0.00009352285,0.0003116187],"category_scores_gemma":[0.00002613705,0.0001535447,0.0001424188,0.0001349213,0.00004832402,0.0002628207,0.00004546583,0.0002753576,0.00000670131],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001603407,"about_ca_system_score_gemma":0.00002361318,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000389357,"about_ca_topic_score_gemma":0.000006152464,"domain_scores_codex":[0.9983115,0.00003026624,0.0007951536,0.0001566789,0.0004454359,0.0002609881],"domain_scores_gemma":[0.9990103,0.00009933375,0.0004924681,0.0002147757,0.0000606937,0.0001224136],"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":[0.003996228,0.01128847,0.008704913,0.001470615,0.003148402,0.0005627624,0.04727279,0.0003733412,0.02618368,0.6093342,0.02301749,0.2646471],"study_design_scores_gemma":[0.02546403,0.003400126,0.04539495,0.0004364648,0.001469407,0.0007466432,0.01611952,0.0001273466,0.02310458,0.8747304,0.007610467,0.001396073],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9974208,0.0003332039,0.0001692533,0.00004951202,0.00006341443,0.0002582549,0.000003175557,0.00001614427,0.001686235],"genre_scores_gemma":[0.9971467,0.0000926296,0.001936677,0.00004447973,0.0003781262,0.0000041518,5.321959e-7,0.00002890895,0.0003677583],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2653962,"threshold_uncertainty_score":0.6261372,"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."}}