{"id":"W2062100222","doi":"10.1016/j.jalgebra.2005.08.005","title":"When is the <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si1.gif\" overflow=\"scroll\"> <mml:mn>2</mml:mn> <mml:mo>×</mml:mo> <mml:mn>2</mml:mn> </mml:math> matrix ring over a commutative local ring strongly clean?","year":2005,"lang":"lv","type":"article","venue":"Journal of Algebra","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":40,"is_retracted":false,"has_abstract":false,"ca_institutions":"Memorial University of Newfoundland","funders":"Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China; Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China","keywords":"Mathematics; Ring (chemistry); Combinatorics; Matrix (chemical analysis); Commutative ring; Prime (order theory); Ideal (ethics); Commutative property; Discrete mathematics; Chemistry; Law","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002128926,0.0002668287,0.0008573552,0.0008069932,0.00274884,0.007454043,0.00083412,0.002768263,0.03526132],"category_scores_gemma":[0.01011445,0.0004687372,0.0007613545,0.0005797352,0.006320294,0.01775895,0.001859836,0.002797262,0.01599987],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001366029,"about_ca_system_score_gemma":0.001593395,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002112249,"about_ca_topic_score_gemma":0.002517019,"domain_scores_codex":[0.9987488,0.0002567432,0.00005302913,0.0003312368,0.0002515925,0.0003586616],"domain_scores_gemma":[0.9957433,0.001206406,0.0004054819,0.0006047594,0.001255178,0.0007848868],"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":[0.0007534052,0.0002022462,0.005183718,0.0004594044,0.00009216733,0.0005812569,0.004229139,0.0002848054,0.007256616,0.8462625,0.08088235,0.05381232],"study_design_scores_gemma":[0.00008483818,0.000113562,0.005713077,0.0002588347,0.00008539324,0.0008824548,0.01200991,0.001497908,0.01571042,0.7371095,0.2263905,0.0001435993],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.2190338,0.006285075,0.1121661,0.1505047,0.00460321,0.0002604331,0.003373025,0.003195842,0.5005779],"genre_scores_gemma":[0.8990129,0.003018585,0.01674081,0.0037968,0.001383959,0.00007491351,0.001705065,0.0008610722,0.07340583],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.03526132,"threshold_uncertainty_score":0.1179609,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02023373198722489,"score_gpt":0.2616125547811787,"score_spread":0.2413788227939538,"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."}}