{"id":"W2043657727","doi":"10.1016/j.jfa.2009.05.003","title":"Sufficient conditions for the projective freeness of Banach algebras","year":2009,"lang":"en","type":"article","venue":"Journal of Functional Analysis","topic":"Holomorphic and Operator Theory","field":"Mathematics","cited_by":31,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Calgary","funders":"","keywords":"Mathematics; Pure mathematics; Maximal ideal; Ideal (ethics); Unital; Banach algebra; Commutative ring; Bounded function; Holomorphic function; Ring (chemistry); Discrete mathematics; Commutative property; Banach space; Algebra over a field; Mathematical analysis","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":[0.00407877,0.001493979,0.001953173,0.003042784,0.00232275,0.00414948,0.00230545,0.002923914,0.0157597],"category_scores_gemma":[0.02076697,0.001683164,0.002271838,0.001229601,0.006707745,0.009974629,0.006407916,0.006734755,0.001594749],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001246764,"about_ca_system_score_gemma":0.002199319,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009687573,"about_ca_topic_score_gemma":0.00104276,"domain_scores_codex":[0.9969041,0.000703613,0.0003616858,0.000684424,0.0007328907,0.0006133315],"domain_scores_gemma":[0.9754778,0.01479759,0.001511572,0.001547136,0.003912628,0.00275317],"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":[0.0002154163,0.00009171008,0.0009953711,0.0001971161,0.00008627863,0.0006025014,0.0006242482,0.00193713,0.004410733,0.9848502,0.002461829,0.003527546],"study_design_scores_gemma":[0.0001475924,0.00006639509,0.001481425,0.00004697233,0.00004640976,0.0004236696,0.0003946422,0.005525008,0.003382199,0.9839521,0.004469238,0.00006435074],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4859564,0.003537135,0.3325043,0.01191894,0.001292273,0.0004102095,0.005215388,0.001184444,0.1579809],"genre_scores_gemma":[0.9685307,0.0009528195,0.01982706,0.0007869769,0.0009834702,0.000289053,0.002111431,0.0001713532,0.006347219],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0157597,"threshold_uncertainty_score":0.05272144,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05292338318044205,"score_gpt":0.3294419646802897,"score_spread":0.2765185814998476,"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."}}