{"id":"W2355916829","doi":"","title":"Excellent Extensions of Rings and Gorenstein Homological Dimension on Smash Product","year":2009,"lang":"en","type":"article","venue":"Journal of Gansu Normal Colleges","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Science North","funders":"","keywords":"Dimension (graph theory); Mathematics; Pure mathematics; Global dimension; Product (mathematics); Local ring; Ring (chemistry); Geometry","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003171487,0.000156713,0.0004500244,0.0001153857,0.00009639847,0.00001540096,0.0001436003,0.00008292563,0.00002806726],"category_scores_gemma":[0.000259855,0.0001043608,0.0001232919,0.0001204288,0.00006909922,0.00008740326,0.0000436829,0.0002685815,6.334481e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002707022,"about_ca_system_score_gemma":0.00004286954,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003153328,"about_ca_topic_score_gemma":0.000001071049,"domain_scores_codex":[0.9986805,0.00006675527,0.0005427126,0.0001381695,0.0003939049,0.0001779327],"domain_scores_gemma":[0.9988312,0.0002098573,0.0004323584,0.0001756022,0.0002400371,0.0001109399],"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":[0.002566685,0.001508508,0.003434693,0.0001777626,0.0002160308,0.000419349,0.001710984,0.0001925222,0.02203683,0.9475424,0.01204135,0.008152844],"study_design_scores_gemma":[0.00342629,0.007692518,0.0663335,0.0005762015,0.0002287124,0.0007209094,0.000442869,0.00008445475,0.03963247,0.8793965,0.001023554,0.0004420162],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9974692,0.0004572987,0.00003900054,0.0009910689,0.0003839194,0.0001378035,0.000001949176,0.00001023668,0.0005094989],"genre_scores_gemma":[0.9975786,0.0001303952,0.001829758,0.00008830931,0.0001990353,6.173171e-7,1.836141e-7,0.000009071622,0.0001640202],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.06814594,"threshold_uncertainty_score":0.4255708,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02626008615611847,"score_gpt":0.2782400284971764,"score_spread":0.251979942341058,"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."}}