{"id":"W2513216252","doi":"10.4153/cmb-2015-082-6","title":"A Note on Algebras that are Sums of Two Subalgebras","year":2015,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Class (philosophy); Associative property; Polynomial; Pure mathematics; Field (mathematics); Semiprime; Algebra over a field; Identity (music); Discrete mathematics; Combinatorics; Prime (order theory)","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0007030963,0.0003653948,0.0006870226,0.0002550073,0.00008474456,0.00004199647,0.0005649092,0.0002071026,0.004659027],"category_scores_gemma":[0.004183306,0.00033418,0.0001656416,0.0002378693,0.0002599256,0.00004718219,0.00008310164,0.000409013,0.006210865],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004236861,"about_ca_system_score_gemma":0.0003338441,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003518831,"about_ca_topic_score_gemma":0.002183235,"domain_scores_codex":[0.9974831,0.0001224458,0.0005890065,0.000425528,0.0006556166,0.000724248],"domain_scores_gemma":[0.9962335,0.001088652,0.0002908085,0.0009894099,0.0001935913,0.001204],"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":[0.00001635299,0.0000844258,0.0001954307,0.0001660541,0.0000292776,0.0001065557,0.0004738106,0.000003027619,0.00002082464,0.9667403,0.03180393,0.0003600823],"study_design_scores_gemma":[0.0008089669,0.00009046413,0.00005266676,0.0002869252,0.00004360856,0.00003848904,0.0002953939,0.00005501008,0.002549587,0.9740786,0.02133599,0.0003643018],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7728589,0.0001853105,0.02076996,0.01604295,0.0006426434,0.001614742,0.0001514496,0.0003692265,0.1873648],"genre_scores_gemma":[0.9529946,0.00000287379,0.04149265,0.001405327,0.0001853971,0.00005325682,0.000007619029,0.0001188386,0.003739482],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1836253,"threshold_uncertainty_score":0.999911,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07413810155515542,"score_gpt":0.3208774762984397,"score_spread":0.2467393747432842,"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."}}