{"id":"W2108905056","doi":"10.1142/s0219498816501486","title":"Rings in which every element is either a sum or a difference of a nilpotent and an idempotent","year":2015,"lang":"en","type":"article","venue":"Journal of Algebra and Its Applications","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":39,"is_retracted":false,"has_abstract":true,"ca_institutions":"Memorial University of Newfoundland","funders":"","keywords":"Mathematics; Idempotence; Matrix ring; Division ring; Ring (chemistry); Nilpotent; Pure mathematics; Noncommutative ring; Element (criminal law); Primitive ring; Unital; Reduced ring; Principal ideal ring; Abelian group; Commutative property; Algebra over a field; Commutative ring; Division (mathematics); Arithmetic; Chemistry; Invertible matrix; Law","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":[0.00053206,0.0001227731,0.0003069625,0.0001379626,0.00004014366,0.00003335518,0.0001499161,0.00005587226,0.00002048505],"category_scores_gemma":[0.0001068641,0.00008659471,0.00003544176,0.0001801947,0.0000351249,0.0001776306,0.00006241041,0.0001505279,0.000001495417],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003323057,"about_ca_system_score_gemma":0.0001020369,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002227046,"about_ca_topic_score_gemma":0.00006889664,"domain_scores_codex":[0.9988208,0.00003562839,0.0005691722,0.0001542919,0.0002591016,0.0001610091],"domain_scores_gemma":[0.998876,0.00009246422,0.0003950897,0.0001672183,0.0002796273,0.000189596],"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":[0.001302009,0.008303469,0.07954365,0.001900157,0.0009065342,0.00004925086,0.0695832,0.0000464648,0.03763756,0.7203239,0.009027055,0.07137678],"study_design_scores_gemma":[0.007392381,0.0025684,0.1835427,0.001026323,0.0004934093,0.00057107,0.007236915,0.003783863,0.01333653,0.7662041,0.01282865,0.001015705],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9945499,0.0006915106,0.003198864,0.001136179,0.00001974719,0.0002793621,0.000005826079,0.000006631492,0.000111933],"genre_scores_gemma":[0.9958121,0.0004046496,0.003346577,0.0001207225,0.00008170329,0.00002671957,6.572996e-7,0.00001396076,0.0001928873],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1039991,"threshold_uncertainty_score":0.353123,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06152216526202526,"score_gpt":0.3204091674727904,"score_spread":0.2588870022107651,"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."}}