{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007342072,0.0003245605,0.0004871777,0.001677353,0.001118546,0.001411152,0.0004538891,0.0003639599,0.003336067],"category_scores_gemma":[0.001129211,0.000277359,0.000429965,0.000647355,0.002368542,0.003146814,0.002156286,0.0008675751,0.0002316528],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006960323,"about_ca_system_score_gemma":0.000282932,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004787019,"about_ca_topic_score_gemma":0.0004168653,"domain_scores_codex":[0.9993883,0.0001308339,0.00003461938,0.0001522865,0.00013514,0.0001587659],"domain_scores_gemma":[0.9989408,0.00022295,0.0002435111,0.0001041409,0.0001266676,0.0003619705],"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":[0.0001554205,0.00004936114,0.005970765,0.00005998809,0.0000299914,0.0004194579,0.000835003,0.001118616,0.005264962,0.978932,0.0006110318,0.006553417],"study_design_scores_gemma":[0.00007519436,0.0002532428,0.02080122,0.00003690627,0.00006807122,0.001685235,0.0008021443,0.006933442,0.005763598,0.9552351,0.00828134,0.00006448555],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.971031,0.0003745607,0.0080973,0.0002938914,0.00003108281,0.00001116831,0.00007622137,0.00004747026,0.0200372],"genre_scores_gemma":[0.9956993,0.0001170837,0.001492561,0.00003182907,0.00005670218,0.00001146681,0.00006932113,0.000005381266,0.00251621],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003336067,"threshold_uncertainty_score":0.01116025,"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."}}