{"id":"W2501721175","doi":"10.1142/s0219498817501523","title":"On ∗-clean group rings over abelian groups","year":2016,"lang":"en","type":"article","venue":"Journal of Algebra and Its Applications","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Brock University; University of California, Santa Cruz","keywords":"Mathematics; Abelian group; Idempotence; Group ring; Group (periodic table); Pure mathematics; Order (exchange); Cyclic group; Combinatorics; Physics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002304495,0.0009875901,0.000928779,0.003129885,0.002300676,0.002632186,0.0007313305,0.0007860868,0.004427026],"category_scores_gemma":[0.003427553,0.0007109996,0.001279521,0.003057353,0.005968089,0.01115227,0.003657714,0.001866821,0.001123899],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008891057,"about_ca_system_score_gemma":0.0005861181,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006209627,"about_ca_topic_score_gemma":0.0003996358,"domain_scores_codex":[0.9979023,0.0005878817,0.0001501742,0.0004514535,0.0005084112,0.0003998047],"domain_scores_gemma":[0.9966201,0.001198163,0.0007773414,0.0005730105,0.0003999808,0.0004314265],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.00009080804,0.00004114395,0.0007291438,0.0001182558,0.00001855646,0.0002732778,0.000688987,0.001316897,0.002469326,0.9854988,0.0007664874,0.007988472],"study_design_scores_gemma":[0.000026268,0.000120102,0.001420201,0.00004387452,0.00003131754,0.000479039,0.0002838811,0.00395651,0.001889034,0.9787841,0.01291241,0.00005315748],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5948945,0.01452199,0.2766321,0.002751368,0.0006840392,0.0001664059,0.0006498694,0.0005403452,0.1091594],"genre_scores_gemma":[0.9355124,0.005821399,0.04335645,0.0004924624,0.0024819,0.0001136027,0.0004462053,0.0001173748,0.01165819],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004427026,"threshold_uncertainty_score":0.01480985,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02019055770144037,"score_gpt":0.2704971962967581,"score_spread":0.2503066385953178,"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."}}