{"id":"W17731821","doi":"10.1090/tran/6815","title":"Homological dimensions for co-rank one idempotent subalgebras","year":2015,"lang":"en","type":"preprint","venue":"Transactions of the American Mathematical Society","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of New Brunswick","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Idempotence; Noetherian; Algebraically closed field; Pure mathematics; Subalgebra; Finitely-generated abelian group; Degree (music); Jacobson radical; Rank (graph theory); Dimension (graph theory); Global dimension; Associative property; Class (philosophy); Ring (chemistry); Combinatorics; Algebra over a field; Physics","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0009925058,0.0005314331,0.001584928,0.00004512618,0.0003200574,0.00003324393,0.001191166,0.0003600692,0.0001744536],"category_scores_gemma":[0.0008715702,0.0003861872,0.001973865,0.0003298886,0.001922979,0.00005782565,0.0002315191,0.001301643,0.00001944507],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003295065,"about_ca_system_score_gemma":0.0002589468,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002041078,"about_ca_topic_score_gemma":0.000003798886,"domain_scores_codex":[0.996661,0.0002116689,0.001116938,0.0006248362,0.0008221912,0.0005633407],"domain_scores_gemma":[0.9940071,0.002520076,0.001067867,0.001788199,0.0003826462,0.0002341721],"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":[0.0003658421,0.00870171,0.0001124376,0.007236773,0.005082822,0.000003706177,0.007623584,0.002427338,0.003025488,0.935001,0.02506288,0.005356402],"study_design_scores_gemma":[0.0004530074,0.0001669569,0.00005402917,0.0002567614,0.0008415481,0.00001245578,0.000571832,0.001864396,0.001689317,0.9934505,0.0002148215,0.000424436],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.1272811,0.00009178265,0.8665347,0.002396755,0.000248255,0.002009176,0.0003805378,0.0002505254,0.0008071541],"genre_scores_gemma":[0.3772523,0.0001020126,0.6208158,0.0003017269,0.0001352965,0.0005408694,0.00001579522,0.0001231582,0.0007131199],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.2499712,"threshold_uncertainty_score":0.999859,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09595709911145325,"score_gpt":0.3684860619704255,"score_spread":0.2725289628589722,"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."}}