{"id":"W2057579366","doi":"10.1016/j.jalgebra.2006.08.012","title":"Group rings in which every element is uniquely the sum of a unit and an idempotent","year":2006,"lang":"en","type":"article","venue":"Journal of Algebra","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":41,"is_retracted":false,"has_abstract":false,"ca_institutions":"Memorial University of Newfoundland; University of Calgary","funders":"Ministry of Education of the People's Republic of China; Natural Sciences and Engineering Research Council of Canada; Natural Science Foundation of Jiangsu Province; National Natural Science Foundation of China","keywords":"Mathematics; Idempotence; Unit (ring theory); Combinatorics; Modulo; Lift (data mining); Element (criminal law); Group ring; Ring (chemistry); Converse; Group (periodic table); Boolean ring; Discrete mathematics; Quotient ring; Commutative ring; Commutative property","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":[0.002301913,0.0006315181,0.0007699127,0.001422077,0.002326058,0.003763534,0.0008137554,0.000940187,0.004184328],"category_scores_gemma":[0.002463914,0.0004916368,0.0007891475,0.001144886,0.005043559,0.008212947,0.002880061,0.001990793,0.002069226],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004551792,"about_ca_system_score_gemma":0.0007863363,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001758948,"about_ca_topic_score_gemma":0.0002705349,"domain_scores_codex":[0.9979973,0.0005968283,0.0001635716,0.000392442,0.0004841924,0.0003656037],"domain_scores_gemma":[0.9983994,0.000335733,0.0002917849,0.000512699,0.0002383919,0.0002218517],"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":[0.0000831923,0.00003596578,0.0002409842,0.00005336527,0.00002982072,0.0001882889,0.0006308439,0.0001613322,0.003494046,0.9829411,0.001327621,0.01081337],"study_design_scores_gemma":[0.00004946413,0.0001286717,0.0003432427,0.00002222937,0.00006374087,0.0008715032,0.0003694827,0.0006879086,0.00838118,0.9553595,0.03368129,0.00004189419],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3237564,0.002476279,0.4789405,0.001370617,0.001897592,0.0002560806,0.0005690656,0.001420342,0.1893131],"genre_scores_gemma":[0.8520109,0.00126315,0.1068593,0.0005589326,0.0009839821,0.000183303,0.0003584784,0.0002016878,0.0375802],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004184328,"threshold_uncertainty_score":0.01399797,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02813431625571882,"score_gpt":0.2820030207897299,"score_spread":0.2538687045340111,"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."}}